Hitting times for special patterns in the symmetric exclusion process on Zd

• 成果类型: Article
• 署名作者: Asselah, A; Pra, PD
• 署名单位: Aix-Marseille Universite; University of Padua
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117904000000487
• 发表日期: 2004
• 页码: 3301-3323
• 关键词: quasi-stationary measures; particle-systems

摘要

We consider the symmetric exclusion process {eta(t), t > 0} on {0,1}(Zd). We fix a pattern A := {eta: Sigma(Lambda) eta(i) greater than or equal to k}, where Lambda is a finite subset of Z(d) and k is an integer, and we consider the problem of establishing sharp estimates for tau, the hitting time of A. We present a novel argument based on monotonicity which helps in some cases to obtain sharp tail asymptotics for tau in a simple way. Also, we characterize the trajectories {eta(s), s less than or equal to t} conditioned on (T > t).