On the tail of the branching random walk local time

• 成果类型: Article
• 署名作者: Angel, Omer; Hutchcroft, Tom; Jarai, Antal
• 署名单位: University of British Columbia; University of Cambridge; University of Bath
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-01014-4
• 发表日期: 2021
• 页码: 467-494
• 关键词: abelian sandpile model; BEHAVIOR; range; limit

摘要

Consider a critical branching random walk on Z(d), d >= 1, started with a single particle at the origin, and let L(x) be the total number of particles that ever visit a vertex x. We study the tail of L(x) under suitable conditions on the offspring distribution. In particular, our results hold if the offspring distribution has an exponential moment.