CONVERGENCE IN LAW FOR THE CAPACITY OF THE RANGE OF A CRITICAL BRANCHING RANDOM WALK
成果类型：
Article
署名作者：
Bai, Tianyi; Hu, Yueyun
署名单位：
New York University; NYU Shanghai
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
DOI：
10.1214/23-AAP1938
发表日期：
2023
页码：
4964-4994
关键词：
摘要：
Let R-n be the range of a critical branching random walk with n particles on Z(d) , which is the set of sites visited by a random walk indexed by a critical Galton- Watson tree conditioned on having exactly n vertices. For d is an element of {3, 4, 5}, we prove that n - (d-2)/(4) cap((d)) (R-n), the renormalized capacity of Rn, converges in law to the capacity of the support of the integrated super-Brownian excursion. The proof relies on a study of the intersection probabilities between the critical branching random walk and an independent simple random walk on Z( d) .
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