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Gaboriau </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33653809" target="_blank">On homology torsion growth</a></div> <div> <span class="journal-title">JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9855">1435-9855</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9863">1435-9863</a>)</span>: <span class="journal-volume">27</span> <span class="journal-issue">6</span> <span class="page"> pp 2293-2357 </span> <span class="year">(2025)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.4171/JEMS/1411" target="_blank" href="https://doi.org/10.4171/JEMS/1411"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="163251" target="_blank" href="http://real.mtak.hu/163251"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="001468790800003" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/001468790800003"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="105003070681" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-105003070681"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="https://ems.press/journals/jems/articles/13892617" target="_blank" href="https://ems.press/journals/jems/articles/13892617"> Egyéb URL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="MR4889244" target="_blank" href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR4889244"> Mathematical Reviews </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Applied Mathematics&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 16</span> | Független: 13 | Függő: 3 | Nem jelölt: 0 | WoS jelölt: 6 | Scopus jelölt:&nbsp;2 | WoS/Scopus jelölt:&nbsp;7 | DOI jelölt:&nbsp;10 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33653809&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 3 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33653809</span> | <span class="status-data status-VALIDATED"> Egyeztetett </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Utolsó módosítás: 2026.03.31. 12:15 Szakonyi Erzsebet (RAMKI admin 4) </div> <div class="lockedBy">Központi kezelésű 2024.03.01. 12:01 Vándor Andrea (VA, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Publication Date: 4 January 2024</pre> </div></div> PublicationOther 36971415 APPROVED true 0 false 2026-02-24T00:41:24.524+0000 2026-02-23T18:55:58.441+0000 2026-02-23T18:55:36.198+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 2026-02-23T18:55:58.460+0000 2026-02-23T18:55:58.460+0000 true true 29 29 /api/publicationtype/29 PublicationType 15 true 29 PublicationOther true 10000361 Publication in repository true 29 29 /api/publicationtype/29 PublicationType 15 true 29 PublicationOther /api/subtype/10000361 Csak repozitóriumban hozzáférhető közlemény SubType 1582 true 10000361 true 1 /api/category/1 Category true 1 Miklos, Abert The Uniform Random Walk on graphs, loop processes and graphings 2025 2026 true false false false NONE 2026-02-24 false 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 false 10011747 false false false 2026-05-24T17:55:58.320+0000 Algebra (HRN RAMKI) 3 9 1 3 0 false Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 134272822 /api/authorship/134272822 1 0.33333334 true false Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true Miklos Abert true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 134272823 /api/authorship/134272823 2 0.33333334 false false Author 10094531 /api/author/10094531 Arras Adam true true Adam Arras true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 134272824 /api/authorship/134272824 3 0.33333334 false true Author 10087339 /api/author/10087339 Kim Jaelin true true Jaelin Kim true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 31520624 /api/publicationidentifier/31520624 PlainSource 37 /api/publicationsource/37 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true arXiv http://arxiv.org/abs/@@@ true true 37 true 2512.09166 http://arxiv.org/abs/2512.09166 false true /api/publication/36971415 <div class="PublicationOther Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Miklos Abert (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="HUN-REN Rényi Alfréd Matematikai Kutatóintézet">HRN RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10094531"><a href="/gui2/?type=authors&mode=browse&sel=10094531" target="_blank">Adam Arras (<span class="authorship-author-name">Arras Adam</span> <span class="authorAux-mtmt"> Probability theory and stochastic processes</span>) </a> </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10087339"><a href="/gui2/?type=authors&mode=browse&sel=10087339" target="_blank">Jaelin Kim (<span class="authorship-author-name">Kim Jaelin</span> <span class="authorAux-mtmt"> Algebra</span>) </a> </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;36971415" target="_blank">The Uniform Random Walk on graphs, loop processes and graphings</a></div> <div class="description"> </div> <div class="country"> Megjelenés: <span class="publishedYear">(2025)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:black" title="2512.09166" target="_blank" href="http://arxiv.org/abs/2512.09166"> arXiv </a> </span> </span> <div class="mtid"><span class="long-pub-mtid">Közlemény: 36971415</span> | <span class="status-data status-APPROVED"> Nyilvános </span> Forrás | <span class="type-subtype">Egyéb ( Csak repozitóriumban hozzáférhető közlemény ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData"></span> </div> <div class="lastModified">Utolsó módosítás: 2026.02.23. 19:55 Szakonyi Erzsebet (RAMKI admin 4) </div> </div></div> JournalArticle 33653831 ADMIN_APPROVED true Export Date: 13 September 2023 Funding details: National Science Foundation, NSF, DMS-1611851, DMS-1654114 Funding details: European Research Council, ERC, 648017 Funding details: Israel Science Foundation, ISF, 2095/15 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K109684 Funding text 1: Abert’s work was partially supported by European Research Council (ERC) Consolidator Grant 648017 and National Research, Development and Innovation Office (NKFIH) grant K109684. Bergeron’s work was partially supported by National Science Foundation (NSF) grant DMS-1611851 and CAREER Award DMS-1654114. Gelander’s work was partially supported by Israel Science Foundation (ISF) Moked grant 2095/15. 0 false 2026-02-24T00:41:28.767+0000 2024-01-15T15:18:51.036+0000 2023-02-22T15:41:25.783+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 2025-02-13T13:08:14.813+0000 2023-11-13T13:14:25.399+0000 true 10017714 Vándor Andrea /api/admin/10017714 Admin true 10017714 Admin 10014568 /api/admin/10014568 Vándor Andrea true 10014568 true 2024-04-18T08:04:22.531+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 M., Abert Convergence of normalized Betti numbers in nonpositive curvature true true /api/journal/1351 REVIEWED true false 1351 false 1351 true 0012-7094 1547-7398 Journal FOREIGN 172 4 633 700 633 68 2023 We study the convergence of volume-normalized Betti numbers in Benjamini–Schramm convergent sequences of nonpositively curved manifolds with finite volume. In particular, we show that if X is an irreducible symmetric space of noncompact type, X ≠ ℍ3, and (Mn) is any Benjamini–Schramm convergent sequence of finite-volume X-manifolds, then the normalized Betti numbers bk(Mn)=vol(Mn) converge for all k. As a corollary, if X has higher rank and (Mn) is any sequence of distinct, finite-volume X-manifolds, then the normalized Betti numbers of Mn converge to the L2-Betti numbers of X. This extends our earlier work with Nikolov, Raimbault, and Samet, where we proved the same convergence result for uniformly thick sequences of compact X-manifolds. One of the novelties of the current work is that it applies to all quotients M D Γ\\X where Γ is arithmetic; in particular, it applies when Γ is isotropic. © 2023 Duke University Press. All rights reserved. 2023 true true true false true false GREEN 2026-02-24 true http://real.mtak.hu/163252 15 0 15 10 1 15 15 9 8 13 13 10 10 10 5 0 15 10 15 10 0 4 4 D1 false 10011747 false false false 2023-05-23T14:41:31.327+0000 Algebra (HRN RAMKI) 1 8 1 4 0 true 10014568 Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 106783146 /api/authorship/106783146 1 0.25 true false Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true M. Abert true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783147 /api/authorship/106783147 2 0.25 false false N. Bergeron true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783148 /api/authorship/106783148 3 0.25 false false I. Biringer true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106783149 /api/authorship/106783149 4 0.25 false true T. Gelander true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 24367716 /api/publicationidentifier/24367716 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1215/00127094-2022-0029 https://doi.org/10.1215/00127094-2022-0029 false true PublicationIdentifier 23308867 /api/publicationidentifier/23308867 SwordSource 36 /api/publicationsource/36 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 163252 http://real.mtak.hu/163252 false true PublicationIdentifier 24367717 /api/publicationidentifier/24367717 PlainSource 1 /api/publicationsource/1 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 000955292600001 https://www.webofscience.com/wos/woscc/full-record/000955292600001 false true PublicationIdentifier 24367718 /api/publicationidentifier/24367718 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true 85150595514 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85150595514 false true SjrRating 11395226 /api/sjrrating/11395226 8 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 2601 /api/classificationexternal/2601 true 2601 true D1 DIRECT true true /api/publication/33653831 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">M. Abert (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="Rényi Alfréd Matematikai Kutatóintézet">RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >N. Bergeron </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >I. Biringer </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >T. Gelander </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33653831" target="_blank">Convergence of normalized Betti numbers in nonpositive curvature</a></div> <div> <span class="journal-title">DUKE MATHEMATICAL JOURNAL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0012-7094">0012-7094</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1547-7398">1547-7398</a>)</span>: <span class="journal-volume">172</span> <span class="journal-issue">4</span> <span class="page"> pp 633-700 </span> <span class="year">(2023)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1215/00127094-2022-0029" target="_blank" href="https://doi.org/10.1215/00127094-2022-0029"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="163252" target="_blank" href="http://real.mtak.hu/163252"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000955292600001" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000955292600001"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="85150595514" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85150595514"> Scopus </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 15</span> | Független: 10 | Függő: 5 | Nem jelölt: 0 | WoS jelölt: 9 | Scopus jelölt:&nbsp;8 | WoS/Scopus jelölt:&nbsp;13 | DOI jelölt:&nbsp;15 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33653831&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 4 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33653831</span> | <span class="status-data status-ADMIN_APPROVED"> Admin láttamozott </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">kézi felvitel</span> </div> <div class="lastModified">Utolsó módosítás: 2024.01.15. 16:18 Wolf György (MTMT Központi admin) </div> <div class="lockedBy">Központi kezelésű 2024.04.18. 10:04 Vándor Andrea (VA, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Export Date: 13 September 2023 Funding details: National Science Foundation, NSF, DMS-1611851, DMS-1654114 Funding details: European Research Council, ERC, 648017 Funding details: Israel Science Foundation, ISF, 2095/15 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K1096...</pre> </div></div> JournalArticle 33688250 APPROVED true Export Date: 8 March 2023 0 false 2026-02-24T00:41:30.230+0000 2023-05-05T15:08:14.390+0000 2023-03-08T11:31:27.431+0000 true 10084481 Toroczkai Annamária /api/admin/10084481 Admin true 2024-08-29T07:46:43.622+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Abért, M. Unimodular measures on the space of all Riemannian manifolds true true /api/journal/10003185 REVIEWED true false 10003185 false 10003185 true 1465-3060 1364-0380 Journal FOREIGN 26 5 2295 2404 2295 110 2022 We study unimodular measures on the space Md of all pointed Riemannian d– manifolds. Examples can be constructed from finite-volume manifolds, from mea-sured foliations with Riemannian leaves, and from invariant random subgroups of Lie groups. Unimodularity is preserved under weak* limits, and under certain geometric constraints (eg bounded geometry) unimodular measures can be used to compactify sets of finite-volume manifolds. One can then understand the geometry of manifolds M with large, finite volume by passing to unimodular limits. We develop a structure theory for unimodular measures on Md, characterizing them via invariance under a certain geodesic flow, and showing that they correspond to transverse measures on a foliated “desingularization” of Md. We also give a geometric proof of a compactness theorem for unimodular measures on the space of pointed manifolds with pinched negative curvature, and characterize unimodular measures supported on hyperbolic 3–manifolds with finitely generated fundamental group. © 2022, Mathematical Sciences Publishers. All rights reserved. 2023 true true true false false GREEN 2026-02-24 true https://doi.org/10.2140/gt.2022.26.2295 18 0 13 6 4 13 13 7 6 9 9 4 4 10 8 0 18 10 13 6 0 7 7 D1 false 10011747 false false false 2023-06-06T10:35:23.811+0000 Algebra (HRN RAMKI) 1 8 1 2 0 true Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 106950272 /api/authorship/106950272 1 0.5 true false false Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true Abért M. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 106950273 /api/authorship/106950273 2 0.5 false true false Biringer I. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 23205217 /api/publicationidentifier/23205217 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true GREEN true IDENTICAL 10.2140/gt.2022.26.2295 https://doi.org/10.2140/gt.2022.26.2295 false true PublicationIdentifier 23508524 /api/publicationidentifier/23508524 SwordSource 36 /api/publicationsource/36 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 165021 http://real.mtak.hu/165021 false true PublicationIdentifier 23205216 /api/publicationidentifier/23205216 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true IDENTICAL 85144224227 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85144224227 false true PublicationIdentifier 11572386 /api/publicationidentifier/11572386 PlainSource 37 /api/publicationsource/37 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true arXiv http://arxiv.org/abs/@@@ true true 37 true NO 1606.03360 http://arxiv.org/abs/1606.03360 false 13405780 true SjrRating 11308090 /api/sjrrating/11308090 5 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 2608 /api/classificationexternal/2608 true 2608 true D1 DIRECT true true /api/publication/33688250 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abért M. (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="Rényi Alfréd Matematikai Kutatóintézet">RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Biringer I. </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33688250" target="_blank">Unimodular measures on the space of all Riemannian manifolds</a></div> <div> <span class="journal-title">GEOMETRY & TOPOLOGY</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1465-3060">1465-3060</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1364-0380">1364-0380</a>)</span>: <span class="journal-volume">26</span> <span class="journal-issue">5</span> <span class="page"> pp 2295-2404 </span> <span class="year">(2022)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:blue" title="10.2140/gt.2022.26.2295" target="_blank" href="https://doi.org/10.2140/gt.2022.26.2295"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="165021" target="_blank" href="http://real.mtak.hu/165021"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85144224227" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85144224227"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="1606.03360" target="_blank" href="http://arxiv.org/abs/1606.03360"> arXiv </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Geometry and Topology&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 18</span> | Független: 10 | Függő: 8 | Nem jelölt: 0 | WoS jelölt: 7 | Scopus jelölt:&nbsp;6 | WoS/Scopus jelölt:&nbsp;9 | DOI jelölt:&nbsp;13 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33688250&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 7 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33688250</span> | <span class="status-data status-APPROVED"> Nyilvános </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2023.05.05. 17:08 Szakonyi Erzsebet (RAMKI admin 4) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Export Date: 8 March 2023</pre> </div></div> JournalArticle 33706737 APPROVED true Export Date: 20 March 2023 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Realtanoda Utca 13-15, Hungary; email: abert@renyi.hu Funding details: NKFI-139502 Funding details: European Research Council, ERC, 648017 Funding text 1: This work was partially supported by ERC Consolidator Grant 648017 and the KKP NKFI-139502 Grant. Acknowledgements 0 false 2026-02-24T00:41:30.829+0000 2026-02-23T18:42:15.504+0000 2023-03-20T09:27:57.418+0000 true 10084481 Toroczkai Annamária /api/admin/10084481 Admin true 2026-02-23T18:42:15.772+0000 2026-02-23T18:42:15.772+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Abért, M. Point processes, cost, and the growth of rank in locally compact groups true true /api/journal/1417131 REVIEWED true false 1417131 false 1417131 true 0021-2172 1565-8511 Journal FOREIGN 251 1 48 155 48 108 2022 Let G be a locally compact, second countable, unimodular group that is nondiscrete and noncompact. We explore the ergodic theory of invariant point processes on G. Our first result shows that every free probability measure preserving (pmp) action of G can be realized by an invariant point process. We then analyze the cost of pmp actions of G using this language. We show that among free pmp actions, the cost is maximal on the Poisson processes. This follows from showing that every free point process weakly factors onto any Poisson process and that the cost is monotone for weak factors, up to some restrictions. We apply this to show that G × ℤ has fixed price 1, solving a problem of Carderi. We also show that when G is a semisimple real Lie group, the rank gradient of any Farber sequence of lattices in G is dominated by the cost of the Poisson process of G. The same holds for the symmetric space X of G. This, in particular, implies that if the cost of the Poisson process of the hyperbolic 3-space ℍ3 vanishes, then the ratio of the Heegaard genus and the rank of a hyperbolic 3-manifold tends to infinity over arbitrary expander Farber sequences, in particular, the ratio can get arbitrarily large. On the other hand, if the cost of the Poisson process on ℍ3 does not vanish, it solves the cost versus L2 Betti problem of Gaboriau for countable equivalence relations. © 2022, The Hebrew University of Jerusalem. 2023 true true true false false NONE 2026-02-24 false 3 0 3 2 0 3 3 2 3 3 3 2 2 2 1 0 3 2 3 2 0 5 5 Q1 false 10011747 false false false 2023-06-18T08:29:54.911+0000 Algebra (HRN RAMKI) 2 8 1 2 0 true Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 107065184 /api/authorship/107065184 1 0.5 true false true Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true Abért M. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PersonAuthorship 107065185 /api/authorship/107065185 2 0.5 false true false Author 10066346 /api/author/10066346 Mellick Samuel true true Mellick S. true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false true PublicationIdentifier 23254151 /api/publicationidentifier/23254151 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true IDENTICAL 10.1007/s11856-022-2445-9 https://doi.org/10.1007/s11856-022-2445-9 false true PublicationIdentifier 23254152 /api/publicationidentifier/23254152 PlainSource 1 /api/publicationsource/1 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true IDENTICAL 000943492500002 https://www.webofscience.com/wos/woscc/full-record/000943492500002 false true PublicationIdentifier 23254150 /api/publicationidentifier/23254150 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true IDENTICAL 85149592369 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149592369 false true SjrRating 11306502 /api/sjrrating/11306502 73 0.24 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 2601 /api/classificationexternal/2601 true 2601 true Q1 DIRECT true true /api/publication/33706737 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abért M. ✉ (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="Rényi Alfréd Matematikai Kutatóintézet">RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10066346"><a href="/gui2/?type=authors&mode=browse&sel=10066346" target="_blank">Mellick S. (<span class="authorship-author-name">Mellick Samuel</span> <span class="authorAux-mtmt"> Gráfelmélet</span>) </a> </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;33706737" target="_blank">Point processes, cost, and the growth of rank in locally compact groups</a></div> <div> <span class="journal-title">ISRAEL JOURNAL OF MATHEMATICS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0021-2172">0021-2172</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1565-8511">1565-8511</a>)</span>: <span class="journal-volume">251</span> <span class="journal-issue">1</span> <span class="page"> pp 48-155 </span> <span class="year">(2022)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1007/s11856-022-2445-9" target="_blank" href="https://doi.org/10.1007/s11856-022-2445-9"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000943492500002" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000943492500002"> WoS </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="85149592369" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85149592369"> Scopus </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;Q1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 3</span> | Független: 2 | Függő: 1 | Nem jelölt: 0 | WoS jelölt: 2 | Scopus jelölt:&nbsp;3 | WoS/Scopus jelölt:&nbsp;3 | DOI jelölt:&nbsp;3 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;33706737&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 5 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 33706737</span> | <span class="status-data status-APPROVED"> Nyilvános </span> Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2026.02.23. 19:42 Szakonyi Erzsebet (RAMKI admin 4) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Export Date: 20 March 2023 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Realtanoda Utca 13-15, Hungary; email: abert@renyi.hu Funding details: NKFI-139502 Funding details: European Research Council, ERC, 648017 Funding text 1: This work was partially supported by ERC Cons...</pre> </div></div> JournalArticle 3274018 ADMIN_APPROVED true MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :13 Export Date: 3 January 2019 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :25 Export Date: 8 February 2020 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :34 Export Date: 7 September 2020 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/2 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :36 Export Date: 25 February 2021 Funding details: National Science Foundation, NSF, 1654114 Funding details: Horizon 2020 Framework Programme, H2020, 648017 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/2, EP/I01893X/1 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :36 Export Date: 26 February 2021 Funding details: National Science Foundation, NSF, 1654114 Funding details: Horizon 2020 Framework Programme, H2020, 648017 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/2, EP/I01893X/1 MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, Rehovot, 76100, Israel University College, Oxford, OX1 4BH, United Kingdom Institut de Mathématiques de Toulouse, UMR5219, Université de Toulouse, CNRS, UPS IMT, Toulouse, France Cited By :41 Export Date: 22 May 2021 Funding details: National Science Foundation, NSF, 1654114 Funding details: Horizon 2020 Framework Programme, H2020, 648017 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/2, EP/I01893X/1 0 2018-07-02T22:22:37.000+0000 false 3274018 2026-03-31T10:24:43.852+0000 2023-09-19T17:22:49.285+0000 2015-09-21T09:27:32.000+0000 true 10011747 Abért Miklós /api/author/10011747 Author true 10011747 2025-02-27T12:52:51.320+0000 2019-01-24T13:13:18.333+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Abert, M On the growth of L2-invariants for sequences of lattices in Lie groups true true /api/journal/357 REVIEWED true false 357 false 357 true 0003-486X 1939-8980 Journal FOREIGN 185 3 711 790 711 80 2017 We study the asymptotic behaviour of Betti numbers, twisted torsion and other spectral invariants of sequences of locally symmetric spaces. Our main results are uniform versions of the DeGeorge-Wallach Theorem, of a theorem of Delorme and various other limit multiplicity theorems. A basic idea is to adapt the notion of Benjamini-Schramm convergence (BS-convergence), originally introduced for sequences of finite graphs of bounded degree, to sequences of Riemannian manifolds, and analyze the possible limits. We show that BS-convergence of locally symmetric spaces Γ\G/K implies convergence, in an appropriate sense, of the normalized relative Plancherel measures associated to L2(Γ\G). This then yields convergence of normalized multiplicities of unitary representations, Betti numbers and other spectral invariants. On the other hand, when the corresponding Lie group G is simple and of real rank at least two, we prove that there is only one possible BS-limit; i.e., when the volume tends to infinity, locally symmetric spaces always BS-converge to their universal cover G/K. This leads to various general uniform results. When restricting to arbitrary sequences of congruence covers of a fixed arithmetic manifold we prove a strong quantitative version of BS-convergence, which in turn implies upper estimates on the rate of convergence of normalized Betti numbers in the spirit of Sarnak-Xue. An important role in our approach is played by the notion of Invariant Random Subgroups. 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href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abert M (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="MTA Rényi Alfréd Matematikai Kutatóintézet">MTA RAMKI</span>/Algebra; <span title="MTA Rényi Alfréd Matematikai Kutatóintézet">MTA RAMKI</span>/Csoportok és gráfok - Lendület</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Bergeron N </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Biringer I </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Gelander T </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Nikolov N </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Raimbault J </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Samet I </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;3274018" target="_blank">On the growth of L2-invariants for sequences of lattices in Lie groups</a></div> 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Uncertainty&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 147</span> | Független: 99 | Függő: 48 | Nem jelölt: 0 | WoS jelölt: 116 | Scopus jelölt:&nbsp;111 | WoS/Scopus jelölt:&nbsp;125 | DOI jelölt:&nbsp;128 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;3274018&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 6 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 3274018</span> | <span class="status-data status-ADMIN_APPROVED"> Admin láttamozott </span> <span class="oldId">Régi azonosító: 3274018</span> | Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2023.09.19. 19:22 Ladányi Gusztáv (MTMT API user, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: MTA Alfréd Rényi Institute of Mathematics, Budapest, Hungary Sorbonne Universités, UPMC Université Paris 06, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586 CNRS, Université Paris Diderot, Sorbonne Paris Cité, Paris, FR-75005, France Boston College, Chestnut Hill, MA, United States Faculty of Mathematics an...</pre> </div></div> JournalArticle 3333008 ADMIN_APPROVED true Cited By :1 Export Date: 3 January 2019 Cited By :2 Export Date: 5 September 2019 Funding details: European Research Council, 648017 Funding details: 2095/15 Funding details: Engineering and Physical Sciences Research Council, EP/H045112/1 Funding text 1: Abert's work is supported by a European Research Council Consolidator grant 648017 and a Magyar Tudom?nyos Akad?mia Lend?let Groups and Graph Limits grant. Gelander's work is supported by Israel Science Foundation-Moked grant 2095/15. Nikolov's work is supported by Engineering and Physical Sciences Research Council grant EP/H045112/1 and the Clay Mathematical Institute. Cited By :2 Export Date: 8 February 2020 Funding details: European Research Council, ERC, 648017 Funding details: 2095/15 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 Funding text 1: Abert's work is supported by a European Research Council Consolidator grant 648017 and a Magyar Tudom?nyos Akad?mia Lend?let Groups and Graph Limits grant. Gelander's work is supported by Israel Science Foundation-Moked grant 2095/15. Nikolov's work is supported by Engineering and Physical Sciences Research Council grant EP/H045112/1 and the Clay Mathematical Institute. Cited By :4 Export Date: 25 February 2021 Funding details: 2095/15 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1, EP/H045112/2 Funding details: European Research Council, ERC, 648017 Funding text 1: Abert's work is supported by a European Research Council Consolidator grant 648017 and a Magyar Tudom?nyos Akad?mia Lend?let Groups and Graph Limits grant. Gelander's work is supported by Israel Science Foundation-Moked grant 2095/15. Nikolov's work is supported by Engineering and Physical Sciences Research Council grant EP/H045112/1 and the Clay Mathematical Institute. Cited By :4 Export Date: 26 February 2021 Funding details: 2095/15 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1, EP/H045112/2 Funding details: European Research Council, ERC, 648017 Funding text 1: Abert's work is supported by a European Research Council Consolidator grant 648017 and a Magyar Tudom?nyos Akad?mia Lend?let Groups and Graph Limits grant. Gelander's work is supported by Israel Science Foundation-Moked grant 2095/15. Nikolov's work is supported by Engineering and Physical Sciences Research Council grant EP/H045112/1 and the Clay Mathematical Institute. Cited By :4 Export Date: 22 May 2021 Funding details: 2095/15 Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1, EP/H045112/2 Funding details: European Research Council, ERC, 648017 Funding text 1: Abert's work is supported by a European Research Council Consolidator grant 648017 and a Magyar Tudom?nyos Akad?mia Lend?let Groups and Graph Limits grant. Gelander's work is supported by Israel Science Foundation-Moked grant 2095/15. Nikolov's work is supported by Engineering and Physical Sciences Research Council grant EP/H045112/1 and the Clay Mathematical Institute. 0 2018-07-02T22:24:15.000+0000 false 3333008 2026-03-31T10:29:38.713+0000 2023-11-09T12:41:49.504+0000 2018-02-11T17:59:10.000+0000 true 10011747 Abért Miklós /api/author/10011747 Author true 10011747 2024-06-28T06:57:39.208+0000 2019-01-24T13:14:05.937+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Abert, M Rank, combinatorial cost, and homology torsion growth in higher rank lattices true true /api/journal/1351 REVIEWED true false 1351 false 1351 true 0012-7094 1547-7398 Journal FOREIGN 166 15 2925 2964 2925 40 2017 We investigate the rank gradient and growth of torsion in homology in residually finite groups. As a tool, we introduce a new complexity notion for generating sets, using measured groupoids and combinatorial cost. As an application we prove the vanishing of the above invariants for Farber sequences of subgroups of right-angled groups. A group is right angled if it can be generated by a sequence of elements of infinite order such that any two consecutive elements commute. Most nonuniform lattices in higher rank simple Lie groups are right angled. We provide the first examples of uniform (cocompact) right-angled arithmetic groups in SL(n,ℝ), n ≥ 3, and SO(p, q) for some values of p, q. This is a class of lattices for which the congruence subgroup property is not known in general. 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autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abert M (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="MTA Rényi Alfréd Matematikai Kutatóintézet">MTA RAMKI</span>/Algebra; <span title="MTA Rényi Alfréd Matematikai Kutatóintézet">MTA RAMKI</span>/Csoportok és gráfok - Lendület</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Gelander T </span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Nikolov N </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;3333008" target="_blank">Rank, combinatorial cost, and homology torsion growth in higher rank lattices</a></div> <div> <span class="journal-title">DUKE MATHEMATICAL JOURNAL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0012-7094">0012-7094</a> <a 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href="/gui2/?mode=browse&params=publication;2516658" target="_blank">Kesten's theorem for invariant random subgroups</a></div> <div> <span class="journal-title">DUKE MATHEMATICAL JOURNAL</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0012-7094">0012-7094</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1547-7398">1547-7398</a>)</span>: <span class="journal-volume">163</span> <span class="journal-issue">3</span> <span class="page"> pp 465-488 </span> <span class="year">(2014)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.1215/00127094-2410064" target="_blank" href="https://doi.org/10.1215/00127094-2410064"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="21938" target="_blank" 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class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Cited By :50 Export Date: 25 February 2021 Correspondence Address: Alfréd Rényi Institute of Mathematics, H-1053, Budapest, Hungary Cited By :50 Export Date: 26 February 2021 Correspondence Address: Alfréd Rényi Institute of Mathematics, H-1053, Budapest, Hungary Cited By :56 ...</pre> </div></div> JournalArticle 2123049 ADMIN_APPROVED true Cited By :29 Export Date: 8 February 2020 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 Cited By :35 Export Date: 22 May 2021 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 0 2015-05-12T14:03:17.000+0000 false 2123049 2026-02-24T00:41:42.224+0000 2023-09-19T12:56:50.966+0000 2012-11-21T10:16:04.000+0000 true 10011747 Abért Miklós /api/author/10011747 Author true 10011747 2024-06-28T07:13:50.790+0000 2012-11-21T11:15:08.000+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Abért, M Rank gradient, cost of groups and the rank versus Heegaard genus problem true true /api/journal/10001247 REVIEWED true false 10001247 false 10001247 true 1435-9855 1435-9863 Journal FOREIGN 14 5 1657 1677 1657 21 2012 We study the growth of the rank of subgroups of finite index in residually finite groups, by relating it to the notion of cost. As a by-product, we show that the 'rank vs. Heegaard genus' conjecture on hyperbolic 3-manifolds is incompatible with the 'fixed price problem' in topological dynamics. © European Mathematical Society 2012. 2012 703443 true true true false true false GREEN 2026-02-24 true http://real.mtak.hu/121709 90 0 70 58 5 66 63 59 58 64 64 52 52 76 14 0 90 76 70 58 0 4 4 D1 true 10011747 false false false 2012-11-21T11:15:08.000+0000 2012-11-21T11:09:37.000+0000 Algebra (HRN RAMKI) 1 8 1 2 0 true Language 10002 /api/language/10002 Angol English true 2 true PersonAuthorship 3295697 /api/authorship/3295697 1 0.5 true false Author 10011747 /api/author/10011747 Abért Miklós true 10011747 true Abért M true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false 16028439 true PersonAuthorship 3295698 /api/authorship/3295698 2 0.5 false true Nikolov N true false false AuthorshipType 1 /api/authorshiptype/1 0 true 0 true false 16028438 true PublicationIdentifier 593145 /api/publicationidentifier/593145 PlainSource 6 /api/publicationsource/6 PublicationSourceType 10001 /api/publicationsourcetype/10001 true true true DOI DOI https://doi.org/@@@ true true 6 true false IDENTICAL 10.4171/JEMS/344 https://doi.org/10.4171/JEMS/344 false 368674 true PublicationIdentifier 593143 /api/publicationidentifier/593143 PlainSource 1 /api/publicationsource/1 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true WoS WoS https://www.webofscience.com/wos/woscc/full-record/@@@ true true 1 true false IDENTICAL 000308126300011 https://www.webofscience.com/wos/woscc/full-record/000308126300011 false 951134 true PublicationIdentifier 18483712 /api/publicationidentifier/18483712 SwordSource 36 /api/publicationsource/36 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true REAL REAL http://real.mtak.hu/@@@ true true 36 true GREEN true 121709 http://real.mtak.hu/121709 false true PublicationIdentifier 593144 /api/publicationidentifier/593144 PlainSource 3 /api/publicationsource/3 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Scopus Scopus http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-@@@ true true 3 true false IDENTICAL 84866034563 http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866034563 false 368675 true PublicationIdentifier 15030490 /api/publicationidentifier/15030490 PlainSource 39 /api/publicationsource/39 PublicationSourceType 10006 /api/publicationsourcetype/10006 true true true Teljes dokumentum Full text @@@ true true 39 true NO http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf false 9045523 true PublicationIdentifier 593146 /api/publicationidentifier/593146 PlainSource 7 /api/publicationsource/7 PublicationSourceType 10003 /api/publicationsourcetype/10003 false true true Mathematical Reviews Mathematical Reviews https://mathscinet.ams.org/mathscinet-getitem?mr=@@@ true true 7 true false NO MR2966663 https://mathscinet.ams.org/mathscinet-getitem?mr=MR2966663 false 1137522 true PublicationIdentifier 15016377 /api/publicationidentifier/15016377 PlainSource 37 /api/publicationsource/37 PublicationSourceType 10007 /api/publicationsourcetype/10007 true true true arXiv http://arxiv.org/abs/@@@ true true 37 true NO math/0701361 http://arxiv.org/abs/math/0701361 false 9120431 true Classification 10006 /api/classification/10006 true true Classification 10004 /api/classification/10004 true true Classification 10003 /api/classification/10003 true true Classification 10002 /api/classification/10002 true true Classification 10001 /api/classification/10001 true true SjrRating 5659605 /api/sjrrating/5659605 6 0.1 journal RatingType 10002 /api/ratingtype/10002 sjr true true ClassificationExternal 2604 /api/classificationexternal/2604 true 2604 true D1 DIRECT true 5659605 true /api/publication/2123049 <div class="JournalArticle Publication long-list"> <div class="authors"> <img title="Forrásközlemény" style="float: left" src="/frontend/resources/grid/publication-core-icon.png"> <img title="Idézőközlemény" style="float: left" src="/frontend/resources/grid/publication-citation-icon.png"> <div class="autype autype0"> <span class="author-name" mtid="10011747"><a href="/gui2/?type=authors&mode=browse&sel=10011747" target="_blank">Abért M (<span class="authorship-author-name">Abért Miklós</span> <span class="authorAux-mtmt"> Csoportelmélet</span>) </a> </span> <span class="author-affil"><span title="MTA Rényi Alfréd Matematikai Kutatóintézet">MTA RAMKI</span>/Algebra</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" >Nikolov N </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;2123049" target="_blank">Rank gradient, cost of groups and the rank versus Heegaard genus problem</a></div> <div> <span class="journal-title">JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9855">1435-9855</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1435-9863">1435-9863</a>)</span>: <span class="journal-volume">14</span> <span class="journal-issue">5</span> <span class="page"> pp 1657-1677 </span> <span class="year">(2012)</span> </div> <div class="pub-footer"> <span class="language" xmlns="http://www.w3.org/1999/html">Nyelv: Angol | </span> <span class="identifiers"> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="10.4171/JEMS/344" target="_blank" href="https://doi.org/10.4171/JEMS/344"> DOI </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000308126300011" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000308126300011"> WoS </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="121709" target="_blank" href="http://real.mtak.hu/121709"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="84866034563" target="_blank" href="http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84866034563"> Scopus </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf" target="_blank" href="http://people.maths.ox.ac.uk/grabowski/files/Abert,%20Nikolov%20-%20rank%20gradient%20and%203-manifolds.pdf"> Teljes dokumentum </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="MR2966663" target="_blank" href="https://mathscinet.ams.org/mathscinet-getitem?mr=MR2966663"> Mathematical Reviews </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:black" title="math/0701361" target="_blank" href="http://arxiv.org/abs/math/0701361"> arXiv </a> </span> </span> <OnlyViewableByAuthor><div class="ratings"> <div class="journal-subject">Folyóirat szakterülete: Scopus - Applied Mathematics&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> <div class="journal-subject">Folyóirat szakterülete: Scopus - Mathematics (miscellaneous)&nbsp;&nbsp;&nbsp;SJR indikátor:&nbsp;D1</div> </div></OnlyViewableByAuthor> <div class="publication-citation" style="margin-left: 0.5cm;"> <span title="Nyilvános idézőközlemények összesen, említések nélkül" class="citingPub-count">Nyilvános idéző összesen: 90</span> | Független: 76 | Függő: 14 | Nem jelölt: 0 | WoS jelölt: 59 | Scopus jelölt:&nbsp;58 | WoS/Scopus jelölt:&nbsp;64 | DOI jelölt:&nbsp;63 </div> <div class="publication-citation"> <a target="_blank" href="/api/publication?cond=citations.related;eq;2123049&sort=publishedYear,desc&sort=title"> Idézett közlemények száma: 4 </a> </div> <div class="mtid"><span class="long-pub-mtid">Közlemény: 2123049</span> | <span class="status-data status-ADMIN_APPROVED"> Admin láttamozott </span> <span class="oldId">Régi azonosító: 2123049</span> | Forrás Idéző | <span class="type-subtype">Folyóiratcikk ( Szakcikk ) </span> | <span class="pub-category">Tudományos</span> | <span class="publication-sourceOfData">Scopus</span> </div> <div class="lastModified">Utolsó módosítás: 2023.09.19. 14:56 Ladányi Gusztáv (MTMT API user, admin) </div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Cited By :29 Export Date: 8 February 2020 Correspondence Address: Abért, M.; Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1053 Budapest, Hungary; email: abert@renyi.hu Funding details: Engineering and Physical Sciences Research Council, EPSRC, EP/H045112/1 Cited By :35 Export Date:...</pre> </div></div>