The Poisson boundary of lampshuffler groups

被引：0

作者：

Silva, Eduardo ^{[1
]}

机构：

[1] PSL Res Univ, Ecole Normale Super, Dept Math & Applicat, 45 rue Ulm, F-75005 Paris, France

来源：

MATHEMATISCHE ZEITSCHRIFT | 2024年 / 308卷 / 03期

基金：

欧洲研究理事会;

关键词：

Random walks; Poisson boundary; Finitary symmetric groups; Locally finite groups; RANDOM-WALKS; DISCRETE-GROUPS; COMMENSURATIONS; ISOPERIMETRY; SUBGROUPS; ENTROPY; THEOREM; GROWTH; NUMBER;

D O I：

10.1007/s00209-024-03607-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study random walks on the lampshuffler group FSym(H) (sic) H, where H is a finitely generated group and FSym(H) is the group of finitary permutations of H. We show that for any step distribution mu with a finite first moment that induces a transient random walk on H, the permutation coordinate of the random walk almost surely stabilizes pointwise. Our main result states that for H = Z, the above convergence completely describes the Poisson boundary of the random walk (FSym(Z) (sic) Z, mu).

引用

页数：27

共 50 条

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