## Electronic Journal of Probability

### Some Sufficient Conditions for Infinite Collisions of Simple Random Walks on a Wedge Comb

#### Abstract

In this paper, we give some sufficient conditions for the infinite collisions of independent simple random walks on a wedge comb with profile $\{f(n):n\in\mathbb{Z}\}$. One interesting result is that two independent simple random walks on the wedge comb will collide infinitely many times if $f(n)$ has a growth order as $n\log(n)$. On the other hand, if $\{f(n):n\in\mathbb{Z}\}$ are given by i.i.d. non-negative random variables with finite mean, then for almost all wedge combs with such profile, three independent simple random walks on it will collide infinitely many times

#### Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 49, 1341-1355.

Dates
Accepted: 9 August 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820218

Digital Object Identifier
doi:10.1214/EJP.v16-907

Mathematical Reviews number (MathSciNet)
MR2827462

Zentralblatt MATH identifier
1244.60069

Rights

#### Citation

Chen, Xinxing; Chen, Dayue. Some Sufficient Conditions for Infinite Collisions of Simple Random Walks on a Wedge Comb. Electron. J. Probab. 16 (2011), paper no. 49, 1341--1355. doi:10.1214/EJP.v16-907. https://projecteuclid.org/euclid.ejp/1464820218

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