Transience of simple random walks with linear entropy growth

被引：0

作者：

Morris, Ben ^{[1
]}

Santhakumar, Hamilton Samraj ^{[1
]}

机构：

[1] Univ Calif Davis, Davis, CA 95616 USA

来源：

ELECTRONIC COMMUNICATIONS IN PROBABILITY | 2023年 / 28卷

关键词：

simple random walk; entropy; transience;

D O I：

10.1214/23-ECP532

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Using the technique of evolving sets, we explore the connection between entropy growth and transience for simple random walks on connected infinite graphs with bounded degree. In particular we show that for a simple random walk starting at a vertex x(0), if the entropy after n steps, E-n is at least Cn where the C is independent of x0, then the random walk is transient. We also give an example which demonstrates that the condition of C being independent of x(0) is necessary.

引用

页数：8