Electronic Journal of Probability

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

Xinxing Chen and Dayue Chen

Full-text: Open access

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

Subjects
Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)
Secondary: 60K37: Processes in random environments

Keywords
wedge comb simple random walk infinite collision property local time

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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