LARGE DEVIATIONS FOR THE CONTACT PROCESS IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Garet, Olivier; Marchand, Regine
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Lorraine; Universite de Lorraine; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP840
• 发表日期: 2014
• 页码: 1438-1479
• 关键词: maximal flow-through; tilted cylinders; large numbers; percolation

摘要

The asymptotic shape theorem for the contact process in random environment gives the existence of a norm mu on R-d such that the hitting time t(x) is asymptotically equivalent to mu(x) when the contact process survives. We provide here exponential upper bounds for the probability of the event {t(x)/mu(x) is not an element of[1 - epsilon, 1 + epsilon]); these bounds are optimal for independent random environment. As a special case, this gives the large deviation inequality for the contact process in a deterministic environment, which, as far as we know, has not been established yet.