Random walks in dynamic random environments: A transference principle
Abstract
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.
Cite
@article{arxiv.1211.0830,
title = {Random walks in dynamic random environments: A transference principle},
author = {Frank Redig and Florian Völlering},
journal= {arXiv preprint arXiv:1211.0830},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP819 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org). arXiv admin note: substantial text overlap with arXiv:1106.4181