On the critical branching random walk I: branching capacity and visiting probability

• 成果类型: Article; Early Access
• 署名作者: Zhu, Qingsan
• 署名单位: Nanjing University of Aeronautics & Astronautics
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01530-9
• 发表日期: 2026-08-22
• 关键词: Critical branching random walk; Branching capacity; Branching harmonic measure; Visiting probability; range

摘要

We study critical branching random walks and introduce the branching capacity and related concepts for any finite subset of Zd,d >= 5 . By introducing these concepts, we can obtain analogues of various classical results for random walks. In this paper, we develop the basic properties of the branching capacity and show that it is closely related to the probability of visiting a fixed finite set by a critical branching random walk starting from a distant point, as well as to the conditional distribution of the hitting point(s).