https://m2.mtmt.hu/ hun 2026-05-01 21:07 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. For higher rank simple Lie groups G, we exploit rigidity theory and, in particular, the Nevo-Stück-Zimmer theorem and Kazhdan's property (T), to obtain a complete understanding of the space of IRS's of G. © 2017 Department of Mathematics, Princeton University. 2017 793796 true true true false true false GREEN GREEN 2026-03-31 true http://real.mtak.hu/64994 147 0 131 90 7 129 128 116 111 125 125 88 88 99 48 0 147 99 131 90 0 6 6 Folyóiratcikk Journal Article 24 119 Könyvrészlet Chapter in Book 25 9 Könyv Book 23 3 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 8 Egyéb Miscellaneous 29 8 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 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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> <div> <span class="journal-title">ANNALS OF MATHEMATICS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/0003-486X">0003-486X</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1939-8980">1939-8980</a>)</span>: <span class="journal-volume">185</span> <span class="journal-issue">3</span> <span class="page"> pp 711-790 </span> <span class="year">(2017)</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="10.4007/annals.2017.185.3.1" target="_blank" href="https://doi.org/10.4007/annals.2017.185.3.1"> DOI </a> </span> <span class="id identifier oa_GREEN" title=" Green "> <a style="color:black" title="64994" target="_blank" href="http://real.mtak.hu/64994"> REAL </a> </span> <span class="id identifier oa_none" title="none"> <a style="color:blue" title="000403468100001" target="_blank" href="https://www.webofscience.com/wos/woscc/full-record/000403468100001"> WoS 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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>