Infinite collision property for the three-dimensional uniform spanning tree

IF 0.3 Q4 MATHEMATICS, APPLIED
Satomi Watanabe
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引用次数: 0

Abstract

Let $\mathcal{U}$ be the uniform spanning tree on $\mathbb{Z}^3$, whose probability law is denoted by $\mathbf{P}$. For $\mathbf{P}$-a.s. realization of $\mathcal{U}$, the recurrence of the the simple random walk on $\mathcal{U}$ is proved in [5] and it is also demonstrated in [8] that two independent simple random walks on $\mathcal{U}$ collide infinitely often. In this article, we will give a quantitative estimate on the number of collisions of two independent simple random walks on $\mathcal{U}$, which provides another proof of the infinite collision property of $\mathcal{U}$.
三维均匀生成树的无限碰撞特性
设$\mathcal{U}$为$\mathbb{Z}^3$上的一致生成树,其概率律用$\mathbf{P}$表示。美元\ mathbf {P}主导者——美元。$\mathcal{U}$的实现,在[5]中证明了$\mathcal{U}$上的简单随机游动的递推性,并在[8]中证明了$\mathcal{U}$上的两个独立的简单随机游动经常无限碰撞。本文将给出$\mathcal{U}$上两个独立简单随机漫步的碰撞次数的定量估计,这再次证明了$\mathcal{U}$的无限碰撞性质。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
24 weeks
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