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

Abstract

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

References in corpus (1)

• The range of tree-indexed random walk in low dimensions

Cited by in corpus (3)

• On the critical branching random walk III: the critical dimension
• On the critical branching random walk II: Branching capacity and branching recurrence
• Logarithmic corrections to scaling in the four-dimensional uniform spanning tree