Bent walls for random groups in the square and hexagonal model
We consider two random group models: the hexagonal model and the square model, defined as the quotient of a free group by a random set of reduced words of length four and six respectively. Our first main result is that in this model there exists a sharp density threshold for Kazhdan's Property...
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | |
---|---|
container_issue | |
container_start_page | |
container_title | |
container_volume | |
creator | Odrzygóźdź, Tomasz |
description | We consider two random group models: the hexagonal model and the square
model, defined as the quotient of a free group by a random set of reduced words
of length four and six respectively. Our first main result is that in this
model there exists a sharp density threshold for Kazhdan's Property (T) and it
equals 1/3. Our second main result is that for densities < 3/8 a random group
in the square model with overwhelming probability does not have Property (T).
Moreover, we provide a new version of the Isoperimetric Inequality that
concerns non-planar diagrams and we introduce new geometrical tools to
investigate random groups: trees of loops, diagrams collared by a tree of loops
and specific codimension one structures in the Cayley complex, called bent
hypergraphs. |
doi_str_mv | 10.48550/arxiv.1906.05417 |
format | Article |
fullrecord | <record><control><sourceid>arxiv_GOX</sourceid><recordid>TN_cdi_arxiv_primary_1906_05417</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1906_05417</sourcerecordid><originalsourceid>FETCH-LOGICAL-a677-686b5d1546278a56f4387f8fde5227e2c52458b9c6307ff8a5a73b6475087b7e3</originalsourceid><addsrcrecordid>eNotz81uwjAQBGBfeqhoH6Cn7gskOLbXay6VAPVPQuqFe7QhNkRyYnCgpW9fSnuaw4xG-oR4qGRpHKKccj53n2U1k7aUaCq6FU8LPxzhi2McIaQMmYc29bDN6bQfoRvguPMwHk6cPVwq2Pkzb9PAEfrU-ngnbgLH0d__50SsX57Xy7di9fH6vpyvCrZEhXW2wbZCYxU5RhuMdhRcaD0qRV5tUBl0zWxjtaQQLhMm3VhDKB015PVEPP7dXgH1Pnc95-_6F1JfIfoHCntB_w</addsrcrecordid><sourcetype>Open Access Repository</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype></control><display><type>article</type><title>Bent walls for random groups in the square and hexagonal model</title><source>arXiv.org</source><creator>Odrzygóźdź, Tomasz</creator><creatorcontrib>Odrzygóźdź, Tomasz</creatorcontrib><description>We consider two random group models: the hexagonal model and the square
model, defined as the quotient of a free group by a random set of reduced words
of length four and six respectively. Our first main result is that in this
model there exists a sharp density threshold for Kazhdan's Property (T) and it
equals 1/3. Our second main result is that for densities < 3/8 a random group
in the square model with overwhelming probability does not have Property (T).
Moreover, we provide a new version of the Isoperimetric Inequality that
concerns non-planar diagrams and we introduce new geometrical tools to
investigate random groups: trees of loops, diagrams collared by a tree of loops
and specific codimension one structures in the Cayley complex, called bent
hypergraphs.</description><identifier>DOI: 10.48550/arxiv.1906.05417</identifier><language>eng</language><subject>Mathematics - Geometric Topology ; Mathematics - Group Theory</subject><creationdate>2019-06</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1906.05417$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1906.05417$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Odrzygóźdź, Tomasz</creatorcontrib><title>Bent walls for random groups in the square and hexagonal model</title><description>We consider two random group models: the hexagonal model and the square
model, defined as the quotient of a free group by a random set of reduced words
of length four and six respectively. Our first main result is that in this
model there exists a sharp density threshold for Kazhdan's Property (T) and it
equals 1/3. Our second main result is that for densities < 3/8 a random group
in the square model with overwhelming probability does not have Property (T).
Moreover, we provide a new version of the Isoperimetric Inequality that
concerns non-planar diagrams and we introduce new geometrical tools to
investigate random groups: trees of loops, diagrams collared by a tree of loops
and specific codimension one structures in the Cayley complex, called bent
hypergraphs.</description><subject>Mathematics - Geometric Topology</subject><subject>Mathematics - Group Theory</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotz81uwjAQBGBfeqhoH6Cn7gskOLbXay6VAPVPQuqFe7QhNkRyYnCgpW9fSnuaw4xG-oR4qGRpHKKccj53n2U1k7aUaCq6FU8LPxzhi2McIaQMmYc29bDN6bQfoRvguPMwHk6cPVwq2Pkzb9PAEfrU-ngnbgLH0d__50SsX57Xy7di9fH6vpyvCrZEhXW2wbZCYxU5RhuMdhRcaD0qRV5tUBl0zWxjtaQQLhMm3VhDKB015PVEPP7dXgH1Pnc95-_6F1JfIfoHCntB_w</recordid><startdate>20190612</startdate><enddate>20190612</enddate><creator>Odrzygóźdź, Tomasz</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20190612</creationdate><title>Bent walls for random groups in the square and hexagonal model</title><author>Odrzygóźdź, Tomasz</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a677-686b5d1546278a56f4387f8fde5227e2c52458b9c6307ff8a5a73b6475087b7e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Mathematics - Geometric Topology</topic><topic>Mathematics - Group Theory</topic><toplevel>online_resources</toplevel><creatorcontrib>Odrzygóźdź, Tomasz</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Odrzygóźdź, Tomasz</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bent walls for random groups in the square and hexagonal model</atitle><date>2019-06-12</date><risdate>2019</risdate><abstract>We consider two random group models: the hexagonal model and the square
model, defined as the quotient of a free group by a random set of reduced words
of length four and six respectively. Our first main result is that in this
model there exists a sharp density threshold for Kazhdan's Property (T) and it
equals 1/3. Our second main result is that for densities < 3/8 a random group
in the square model with overwhelming probability does not have Property (T).
Moreover, we provide a new version of the Isoperimetric Inequality that
concerns non-planar diagrams and we introduce new geometrical tools to
investigate random groups: trees of loops, diagrams collared by a tree of loops
and specific codimension one structures in the Cayley complex, called bent
hypergraphs.</abstract><doi>10.48550/arxiv.1906.05417</doi><oa>free_for_read</oa></addata></record> |
fulltext | fulltext_linktorsrc |
identifier | DOI: 10.48550/arxiv.1906.05417 |
ispartof | |
issn | |
language | eng |
recordid | cdi_arxiv_primary_1906_05417 |
source | arXiv.org |
subjects | Mathematics - Geometric Topology Mathematics - Group Theory |
title | Bent walls for random groups in the square and hexagonal model |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2024-12-25T20%3A39%3A59IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-arxiv_GOX&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Bent%20walls%20for%20random%20groups%20in%20the%20square%20and%20hexagonal%20model&rft.au=Odrzyg%C3%B3%C5%BAd%C5%BA,%20Tomasz&rft.date=2019-06-12&rft_id=info:doi/10.48550/arxiv.1906.05417&rft_dat=%3Carxiv_GOX%3E1906_05417%3C/arxiv_GOX%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_id=info:pmid/&rfr_iscdi=true |