Some sufficient conditions for infinite collisions of simple random walks on a wedge comb

Xinxing Chen; Dayue Chen

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arXiv · 1010.5366

Some sufficient conditions for infinite collisions of simple random walks on a wedge comb

Xinxing Chen·Dayue Chen

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Abstract

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

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BibTeX RIS

Xinxing Chen, Dayue Chen. 2010-10-26. Some sufficient conditions for infinite collisions of simple random walks on a wedge comb. https://arxiv.org/abs/1010.5366

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