LARGE DEVIATIONS FOR RANDOM WALK IN A SPACE-TIME PRODUCT ENVIRONMENT

• 成果类型: Article
• 署名作者: Yilmaz, Atilla
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/08-AOP400
• 发表日期: 2009
• 页码: 189-205
• 关键词: reversible markov-processes

摘要

We consider random walk (X(n))(n >= 0) on Z(d) in a space-time product environment omega is an element of Omega. We take the point of view of the particle and focus on the environment Markov chain (T(n),X(n)omega)(n >= 0) where T denotes the shift on Omega. Conditioned on the particle having asymptotic mean velocity equal to any given xi, we show that the empirical process of the environment Markov chain converges to a stationary process mu(infinity)(xi) under the averaged measure. When d >= 3 and xi is sufficiently close to the typical velocity, we prove that averaged and quenched large deviations are equivalent and when conditioned on the particle having asymptotic mean velocity xi, the empirical process of the environment Markov chain converges to mu(infinity)(xi)under the quenched measure as well. In this case, we show that mu(infinity)(xi) is a stationary Markov process whose kernel is obtained from the original kernel by a Doob h-transform.