Tracking rates of random walks
We show that simple random walks on (non-trivial) relatively hyperbolic groups stay O (log( n ))-close to geodesics, where n is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay O ( n log ( n ) ) -close to geodesics and hierarchy...
Gespeichert in:
| Veröffentlicht in: | Israel journal of mathematics 2017-06, Vol.220 (1), p.1-28 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 28 |
|---|---|
| container_issue | 1 |
| container_start_page | 1 |
| container_title | Israel journal of mathematics |
| container_volume | 220 |
| creator | Sisto, Alessandro |
| description | We show that simple random walks on (non-trivial) relatively hyperbolic groups stay
O
(log(
n
))-close to geodesics, where
n
is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay
O
(
n
log
(
n
)
)
-close to geodesics and hierarchy paths. Along the way, we also prove a refinement of the result that mapping class groups have quadratic divergence.
An application of our theorem for relatively hyperbolic groups is that random triangles in non-trivial relatively hyperbolic groups are
O
(log(
n
))-thin, random points have
O
(log(
n
))-small Gromov product and that in many cases the average Dehn function is subasymptotic to the Dehn function. |
| doi_str_mv | 10.1007/s11856-017-1508-9 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_journals_1914590158</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1914590158</sourcerecordid><originalsourceid>FETCH-LOGICAL-c316t-7da450fa19e2ab67ee2105390e40bf278cdccfe02477b2404b148c00dffab27b3</originalsourceid><addsrcrecordid>eNp1kE1LAzEURYMoWKs_wI0MuI6-l0kmyVKKVqHgpq5DkklKv2ZqMkX896aMCzeu3lvccy8cQm4RHhBAPmZEJRoKKCkKUFSfkQmKRlAlEM_JBIAhZSjZJbnKeQMgaon1hNwtk_Xbdbeqkh1CrvpYnq7t99WX3W3zNbmIdpfDze-dko-X5-XslS7e52-zpwX1NTYDla3lAqJFHZh1jQyBYVnQEDi4yKTyrfcxAONSOsaBO-TKA7QxWsekq6fkfuw9pP7zGPJgNv0xdWXSoEYuNKBQJYVjyqc-5xSiOaT13qZvg2BOGsyowRQN5qTB6MKwkckl261C-tP8L_QDfTZd5w</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1914590158</pqid></control><display><type>article</type><title>Tracking rates of random walks</title><source>SpringerLink Journals - AutoHoldings</source><creator>Sisto, Alessandro</creator><creatorcontrib>Sisto, Alessandro</creatorcontrib><description>We show that simple random walks on (non-trivial) relatively hyperbolic groups stay
O
(log(
n
))-close to geodesics, where
n
is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay
O
(
n
log
(
n
)
)
-close to geodesics and hierarchy paths. Along the way, we also prove a refinement of the result that mapping class groups have quadratic divergence.
An application of our theorem for relatively hyperbolic groups is that random triangles in non-trivial relatively hyperbolic groups are
O
(log(
n
))-thin, random points have
O
(log(
n
))-small Gromov product and that in many cases the average Dehn function is subasymptotic to the Dehn function.</description><identifier>ISSN: 0021-2172</identifier><identifier>EISSN: 1565-8511</identifier><identifier>DOI: 10.1007/s11856-017-1508-9</identifier><language>eng</language><publisher>Jerusalem: The Hebrew University Magnes Press</publisher><subject>Algebra ; Analysis ; Applications of Mathematics ; Divergence ; Geodesy ; Group Theory and Generalizations ; Mapping ; Mathematical and Computational Physics ; Mathematics ; Mathematics and Statistics ; Random walk ; Random walk theory ; Theoretical ; Triangles</subject><ispartof>Israel journal of mathematics, 2017-06, Vol.220 (1), p.1-28</ispartof><rights>Hebrew University of Jerusalem 2017</rights><rights>Copyright Springer Science & Business Media 2017</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c316t-7da450fa19e2ab67ee2105390e40bf278cdccfe02477b2404b148c00dffab27b3</citedby><cites>FETCH-LOGICAL-c316t-7da450fa19e2ab67ee2105390e40bf278cdccfe02477b2404b148c00dffab27b3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s11856-017-1508-9$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s11856-017-1508-9$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27923,27924,41487,42556,51318</link.rule.ids></links><search><creatorcontrib>Sisto, Alessandro</creatorcontrib><title>Tracking rates of random walks</title><title>Israel journal of mathematics</title><addtitle>Isr. J. Math</addtitle><description>We show that simple random walks on (non-trivial) relatively hyperbolic groups stay
O
(log(
n
))-close to geodesics, where
n
is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay
O
(
n
log
(
n
)
)
-close to geodesics and hierarchy paths. Along the way, we also prove a refinement of the result that mapping class groups have quadratic divergence.
An application of our theorem for relatively hyperbolic groups is that random triangles in non-trivial relatively hyperbolic groups are
O
(log(
n
))-thin, random points have
O
(log(
n
))-small Gromov product and that in many cases the average Dehn function is subasymptotic to the Dehn function.</description><subject>Algebra</subject><subject>Analysis</subject><subject>Applications of Mathematics</subject><subject>Divergence</subject><subject>Geodesy</subject><subject>Group Theory and Generalizations</subject><subject>Mapping</subject><subject>Mathematical and Computational Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Random walk</subject><subject>Random walk theory</subject><subject>Theoretical</subject><subject>Triangles</subject><issn>0021-2172</issn><issn>1565-8511</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp1kE1LAzEURYMoWKs_wI0MuI6-l0kmyVKKVqHgpq5DkklKv2ZqMkX896aMCzeu3lvccy8cQm4RHhBAPmZEJRoKKCkKUFSfkQmKRlAlEM_JBIAhZSjZJbnKeQMgaon1hNwtk_Xbdbeqkh1CrvpYnq7t99WX3W3zNbmIdpfDze-dko-X5-XslS7e52-zpwX1NTYDla3lAqJFHZh1jQyBYVnQEDi4yKTyrfcxAONSOsaBO-TKA7QxWsekq6fkfuw9pP7zGPJgNv0xdWXSoEYuNKBQJYVjyqc-5xSiOaT13qZvg2BOGsyowRQN5qTB6MKwkckl261C-tP8L_QDfTZd5w</recordid><startdate>20170601</startdate><enddate>20170601</enddate><creator>Sisto, Alessandro</creator><general>The Hebrew University Magnes Press</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20170601</creationdate><title>Tracking rates of random walks</title><author>Sisto, Alessandro</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c316t-7da450fa19e2ab67ee2105390e40bf278cdccfe02477b2404b148c00dffab27b3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Algebra</topic><topic>Analysis</topic><topic>Applications of Mathematics</topic><topic>Divergence</topic><topic>Geodesy</topic><topic>Group Theory and Generalizations</topic><topic>Mapping</topic><topic>Mathematical and Computational Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Random walk</topic><topic>Random walk theory</topic><topic>Theoretical</topic><topic>Triangles</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Sisto, Alessandro</creatorcontrib><collection>CrossRef</collection><jtitle>Israel journal of mathematics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Sisto, Alessandro</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Tracking rates of random walks</atitle><jtitle>Israel journal of mathematics</jtitle><stitle>Isr. J. Math</stitle><date>2017-06-01</date><risdate>2017</risdate><volume>220</volume><issue>1</issue><spage>1</spage><epage>28</epage><pages>1-28</pages><issn>0021-2172</issn><eissn>1565-8511</eissn><abstract>We show that simple random walks on (non-trivial) relatively hyperbolic groups stay
O
(log(
n
))-close to geodesics, where
n
is the number of steps of the walk. Using similar techniques we show that simple random walks in mapping class groups stay
O
(
n
log
(
n
)
)
-close to geodesics and hierarchy paths. Along the way, we also prove a refinement of the result that mapping class groups have quadratic divergence.
An application of our theorem for relatively hyperbolic groups is that random triangles in non-trivial relatively hyperbolic groups are
O
(log(
n
))-thin, random points have
O
(log(
n
))-small Gromov product and that in many cases the average Dehn function is subasymptotic to the Dehn function.</abstract><cop>Jerusalem</cop><pub>The Hebrew University Magnes Press</pub><doi>10.1007/s11856-017-1508-9</doi><tpages>28</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0021-2172 |
| ispartof | Israel journal of mathematics, 2017-06, Vol.220 (1), p.1-28 |
| issn | 0021-2172 1565-8511 |
| language | eng |
| recordid | cdi_proquest_journals_1914590158 |
| source | SpringerLink Journals - AutoHoldings |
| subjects | Algebra Analysis Applications of Mathematics Divergence Geodesy Group Theory and Generalizations Mapping Mathematical and Computational Physics Mathematics Mathematics and Statistics Random walk Random walk theory Theoretical Triangles |
| title | Tracking rates of random walks |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-08T12%3A46%3A55IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Tracking%20rates%20of%20random%20walks&rft.jtitle=Israel%20journal%20of%20mathematics&rft.au=Sisto,%20Alessandro&rft.date=2017-06-01&rft.volume=220&rft.issue=1&rft.spage=1&rft.epage=28&rft.pages=1-28&rft.issn=0021-2172&rft.eissn=1565-8511&rft_id=info:doi/10.1007/s11856-017-1508-9&rft_dat=%3Cproquest_cross%3E1914590158%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1914590158&rft_id=info:pmid/&rfr_iscdi=true |