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
Citation
Xinxing Chen. Dayue Chen. "Some Sufficient Conditions for Infinite Collisions of Simple Random Walks on a Wedge Comb." Electron. J. Probab. 16 1341 - 1355, 2011. https://doi.org/10.1214/EJP.v16-907
Information