Ilya Kapovich, Joseph Maher, Catherine Pfaff, Samuel J. Taylor
{"title":"Random trees in the boundary of outer space","authors":"Ilya Kapovich, Joseph Maher, Catherine Pfaff, Samuel J. Taylor","doi":"10.2140/gt.2022.26.127","DOIUrl":null,"url":null,"abstract":"We prove that for the harmonic measure associated to a random walk on Out$(F_r)$ satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This answers a question of M. Bestvina.","PeriodicalId":254292,"journal":{"name":"Geometry & Topology","volume":"17 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry & Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gt.2022.26.127","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
We prove that for the harmonic measure associated to a random walk on Out$(F_r)$ satisfying some mild conditions, a typical tree in the boundary of Outer space is trivalent and nongeometric. This answers a question of M. Bestvina.