Hitting times for independent random walks on Zd

• 成果类型: Article
• 署名作者: Asselah, Amine; Ferrari, Pablo A.
• 署名单位: Aix-Marseille Universite; Universidade de Sao Paulo
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117906000000106
• 发表日期: 2006
• 页码: 1296-1338
• 关键词: quasi-stationary measures

摘要

We consider a system of asymmetric independent random walks on Z(d), denoted by {eta(t), t is an element of R}, stationary under the product Poisson measure v(rho) of marginal density p > 0. We fix a pattern A, an increasing local event, and denote by tau the hitting time of A. By using a loss network representation of our system, at small density, we obtain a coupling between the laws of eta(t) conditioned on (tau > t) for all times t. When d >= 3, this provides bounds on the rate of convergence of the law of eta(t) conditioned on {tau > t} toward its limiting probability measure as t tends to infinity. We also treat the case where the initial measure is close to v(rho) without being product.