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September 2013 Random walks in dynamic random environments: A transference principle
Frank Redig, Florian Völlering
Ann. Probab. 41(5): 3157-3180 (September 2013). DOI: 10.1214/12-AOP819


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.


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Frank Redig. Florian Völlering. "Random walks in dynamic random environments: A transference principle." Ann. Probab. 41 (5) 3157 - 3180, September 2013.


Published: September 2013
First available in Project Euclid: 12 September 2013

zbMATH: 1277.82051
MathSciNet: MR3127878
Digital Object Identifier: 10.1214/12-AOP819

Primary: 82C41
Secondary: 60F17

Keywords: central limit theorem , coupling , Environment process , Random walk , transference principle

Rights: Copyright © 2013 Institute of Mathematical Statistics


Vol.41 • No. 5 • September 2013
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