An upper bound for the probability of visiting a distant point by critical branching random walk in ℤ⁴

2015/03/01 by Qingsan Zhu, Zhu, Qingsan
Decision Sciences · Mathematics · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1503.00305

openalex publication_date 2015/03/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the probability of visiting a distant point a∈ ℤ⁴ by critical branching random walk starting from the origin. We prove that this probability is bounded by 1/(|a|²log |a|) up to a constant.

Related

• On the critical branching random walk III: the critical dimension
• Branching random walk in Z⁴ with branching at the origin only
• Time spent in a ball by a critical branching random walk
• On the critical branching random walk I: Branching capacity and visiting probability
• Yaglom theorem for critical branching random walk on ℤ^d