RANDOM WALKS IN DYNAMIC RANDOM ENVIRONMENTS: A TRANSFERENCE PRINCIPLE

• 成果类型: Article
• 署名作者: Redig, Frank; Voellering, Florian
• 署名单位: Delft University of Technology; University of Gottingen
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/12-AOP819
• 发表日期: 2013
• 页码: 3157-3180
• 关键词: markovian environment; molecular motors; large numbers; MODEL; LAW

摘要

We study a general class of random walks driven by a uniquely ergodic Markovian environment. Under a coupling condition on the environment we obtain strong ergodicity properties for the environment as seen from the position of the walker, that is, the environment process. We can transfer the rate of mixing in time of the environment to the rate of mixing of the environment process with a loss of at most polynomial order. Therefore the method is applicable to environments with sufficiently fast polynomial mixing. We obtain unique ergodicity of the environment process. Moreover, the unique invariant measure of the environment process depends continuously on the jump rates of the walker. As a consequence we obtain the law of large numbers and a central limit theorem with nondegenerate variance for the position of the walk.