A Non-Symmetric Kesten Criterion and Ratio Limit Theorem for Random Walks on Amenable Groups

被引：0

作者：

Dougall, Rhiannon ^{[1
]}

Sharp, Richard ^{[2
]}

机构：

[1] Univ Durham, Dept Math Sci, Durham DH1 3LE, England

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, England

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2024年 / 2024卷 / 07期

关键词：

THERMODYNAMIC FORMALISM; MARKOV; EXISTENCE;

D O I：

10.1093/imrn/rnae014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue of this result for walks that are not symmetric. We also conclude a ratio limit theorem for amenable groups.

引用

页码：6209 / 6223

页数：15

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