https://m2.mtmt.hu/ hun 2026-05-02 03:52 JournalArticle 34199970 VALIDATED true Division of Mathematics, The Science Institute, University of Iceland, Reykjavik, Iceland Alfréd Rényi Institute of Mathematics, Budapest, Hungary Chair of Ergodic and Geometric Group Theory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Export Date: 27 February 2024 Correspondence Address: Timár, Á.; Division of Mathematics, Iceland; email: madaramit@gmail.com Funding details: European Research Council, ERC, 648017 Funding details: Icelandic Centre for Research, RANNIS, 185233‐051 Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFI, KKP‐139502 Funding text 1: The first author was partially supported by ERC Consolidator Grant 648017 and by Icelandic Research Fund Grant 185233‐051. The second author was partially supported by NKFIH (National Research, Development and Innovation Office, Hungary) grant KKP‐139502, “Groups and graph limits”. 0 false 2026-03-31T17:13:11.081+0000 2024-02-15T13:58:03.853+0000 2023-10-16T15:35:37.418+0000 true 10076734 Tóth László Márton /api/author/10076734 Author true 2024-06-18T00:04:38.845+0000 2024-02-15T13:58:04.023+0000 true 10017714 Vándor Andrea /api/admin/10017714 Admin true 10017714 Admin 10014568 /api/admin/10014568 Vándor Andrea true 10014568 true 2025-05-12T14:53:22.805+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 Timár, Ádám A full characterization of invariant embeddability of unimodular planar graphs true true /api/journal/2050642 REVIEWED true false 2050642 false 2050642 true 1042-9832 1098-2418 Journal FOREIGN 64 2 320 353 320 34 2024 When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry‐invariant? This question was answered for one‐ended unimodular graphs in Benjamini and Timar, using the fact that such graphs automatically have locally finite (simply connected) drawings into the plane. For the case of graphs with multiple ends the question was left open. We revisit Halin's graph theoretic characterization of graphs that have a locally finite embedding into the plane. Then we prove that such unimodular random graphs do have a locally finite invariant embedding into the Euclidean or the hyperbolic plane, depending on whether the graph is amenable or not. true 2023 true true true false true false GREEN 2026-03-31 true https://doi.org/10.1002/rsa.21188 3 0 3 0 2 3 3 3 2 3 3 0 0 0 3 0 3 0 3 0 0 3 3 Folyóiratcikk Journal Article 24 3 Könyvrészlet Chapter in Book 25 0 Könyv Book 23 0 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 0 Egyéb Miscellaneous 29 0 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 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 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title="HUN-REN Rényi Alfréd Matematikai Kutatóintézet">HRN RAMKI</span>/Zaj-érzékenység ERC; Rényi Alfréd Matematikai Kutatóintézet</span> ;&nbsp;&nbsp;&nbsp; <span class="author-name" mtid="10076734"><a href="/gui2/?type=authors&mode=browse&sel=10076734" target="_blank">Tóth László Márton (<span class="authorship-author-name">Tóth László Márton</span> <span class="authorAux-mtmt"> csoportelmélet</span>) </a> </span> </div> </div> <div class="title"><a href="/gui2/?mode=browse&params=publication;34199970" target="_blank">A full characterization of invariant embeddability of unimodular planar graphs</a></div> <div> <span class="journal-title">RANDOM STRUCTURES & ALGORITHMS</span> <span class="journal-issn">(<a target="_blank" href="https://portal.issn.org/resource/ISSN/1042-9832">1042-9832</a> <a target="_blank" href="https://portal.issn.org/resource/ISSN/1098-2418">1098-2418</a>)</span>: <span class="journal-volume">64</span> <span class="journal-issue">2</span> <span class="page"> pp 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</div> <pre class="comment" style="margin-top: 0; margin-bottom: 0;"><u>Megjegyzés</u>: Division of Mathematics, The Science Institute, University of Iceland, Reykjavik, Iceland Alfréd Rényi Institute of Mathematics, Budapest, Hungary Chair of Ergodic and Geometric Group Theory, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland Export Date: 27 February 2024 Correspondence ...</pre> </div></div>