FROM TRANSIENCE TO RECURRENCE WITH POISSON TREE FROGS

• 成果类型: Article
• 署名作者: Hoffman, Christopher; Johnson, Tobias; Junge, Matthew
• 署名单位: University of Washington; University of Washington Seattle; University of Southern California
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1127
• 发表日期: 2016
• 页码: 1620-1635
• 关键词: contact process; random-walk; PHASE-TRANSITION; BEHAVIOR

摘要

Consider the following interacting particle system on the d-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic factor.