Non-intersection of transient branching random walks

• 成果类型: Article
• 署名作者: Hutchcroft, Tom
• 署名单位: University of Cambridge
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-00964-z
• 发表日期: 2020
• 页码: 1-23
• 关键词: critical-behavior; percolation; recurrence; limit; ends

摘要

Let G be a Cayley graph of a nonamenable group with spectral radius rho<1. It is known that branching random walk on G with offspring distribution mu is transient, i.e., visits the origin at most finitely often almost surely, if and only if the expected number of offspring mu over bar satisfies mu over bar <=rho-1. Benjamini and Muller (Groups Geom Dyn, 6:231-247, 2012) conjectured that throughout the transient supercritical phase 1