An upper bound for the probability of visiting a distant point by a critical branching random walk in $\mathbb{Z} ^{4}$

[摘要] In this paper, we study the probability of visiting a distant point $a\in \mathbb{Z} ^{4}$ by a critical branching random walk starting at the origin. We prove that this probability is bounded by $1/(|a|^{2}\log |a|)$ up to a constant factor.

[学科分类] 统计和概率

[关键词] critical branching random walk;visiting probability;critical dimension