A zero-one law for recurrence and transience of frog processes

• 成果类型: Article
• 署名作者: Kosygina, Elena; Zerner, Martin P. W.
• 署名单位: City University of New York (CUNY) System; Baruch College (CUNY); Eberhard Karls University of Tubingen
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-016-0711-7
• 发表日期: 2017
• 页码: 317-346
• 关键词: random-walks; random environment

摘要

We provide sufficient conditions for the validity of a dichotomy, i.e. zero-one law, between recurrence and transience of general frog models. In particular, the results cover frog models with i.i.d. numbers of frogs per site where the frog dynamics are given by quasi-transitive Markov chains or by random walks in a common random environment including super-critical percolation clusters on . We also give a sufficient and almost sharp condition for recurrence of uniformly elliptic frog processes on . Its proof uses the general zero-one law.