Recurrence and ergodicity of interacting particle systems

• 成果类型: Article
• 署名作者: Cox, JT; Klenke, A
• 署名单位: Syracuse University; University of Erlangen Nuremberg
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/PL00008728
• 发表日期: 2000
• 页码: 239-255
• 关键词: voter model; THEOREMS; DIFFUSIONS

摘要

Many interacting particle systems with short range interactions are not ergodic, but converge weakly towards a mixture of their ergodic invariant measures. The question arises whether a.s. the process eventually stays close to one of these ergodic states, or if it changes between the attainable ergodic states infinitely often (recurrence). Under the assumption that there exists a convergence-determining class of distributions that is (strongly) preserved under the dynamics, we show that the system is in fact recurrent in the above sense. We apply our method to several interacting particle systems, obtaining new or improved recurrence results. In addition, we answer a question raised by Ed Perkins concerning the change of the locally predominant type in a model of mutually catalytic branching.