SLLN and annealed CLT for random walks in IID random environment on Cayley trees

被引：0

作者：

Athreya, Siva ^{[1
]}

Bandyopadhyay, Antar ^{[2
,3
]}

Dasgupta, Amites ^{[3
]}

Sahasrabudhe, Neeraja ^{[4
]}

机构：

[1] Indian Stat Inst, Theoret Stat & Math Unit, 8th Mile Mysore Rd, Bangalore 560059, India

[2] Indian Stat Inst, Delhi Ctr, Theoret Stat & Math Unit, 7 SJS Sansanwal Marg, New Delhi 110016, India

[3] Indian Stat Inst, Theoret Stat & Math Unit, BT Rd 203, Kolkata 700108, India

[4] Indian Inst Sci Educ & Res, Dept Math Sci, Sect 81, Sahibzada Ajit Singh Naga 140306, Punjab, India

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2022年 / 146卷

关键词：

Random walk on free group; Random walk in random environment; Trees; Transience; Central limit theorem; Positive speed; GALTON-WATSON TREES; BIASED RANDOM-WALKS; PERCOLATION; SPEED;

D O I：

10.1016/j.spa.2021.12.009

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：

We consider the random walk in an independent and identically distributed (i.i.d.) random environment on a Cayley graph of a finite free product of copies of Z and Z(2). Such a Cayley graph is readily seen to be a regular tree. Under a uniform ellipticity assumption on the i.i.d. environment we show that the walk has positive speed and establish the annealed central limit theorem for the graph distance of the walker from the starting point. (c) 2021 Elsevier B.V. All rights reserved.

引用

页码：80 / 97

页数：18

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