Multidimensional branching random walks in random environment

• 成果类型: Article
• 署名作者: Comets, Francis; Popov, Serguei
• 署名单位: Universite Paris Cite; Universidade de Sao Paulo
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000926
• 发表日期: 2007
• 页码: 68-114
• 关键词: dimensional random-walk; large deviations; large numbers; shape; LAW

摘要

We study branching random walks in random i.i.d. environment in Z(d), d >= 1. For this model, the population size cannot decrease, and a natural definition of recurrence is introduced. We prove a dichotomy for recurrence/transience, depending only on the support of the environmental law. We give sufficient conditions for recurrence and for transience. In the recurrent case, we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of lattice sites which are visited up to a large time.