Einstein relation for random walks in random environment

Abstract

In this article, we consider the speed of the random walks in a (uniformly elliptic and i.i.d.) random environment (RWRE) under perturbation. We obtain the derivative of the speed of the RWRE w.r.t. the perturbation, under the assumption that one of the following holds: (i) the environment is balanced and the perturbation satisfies a Kalikow-type ballisticity condition, (ii) the environment satisfies Sznitman's ballisticity condition. This is a generalized version of the Einstein relation for RWRE. Our argument is based on a modification of Lebowitz-Rost's argument developed in [Stochastic Process. Appl. 54 (1994) 183-196] and a new regeneration structure for the perturbed balanced environment.

Published at http://dx.doi.org/10.1214/14-AOP975 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (5)

• Quenched invariance principle for random walks in balanced random environment
• Ballistic random walks in random environment at low disorder
• Effective Polynomial Ballisticity Condition for Random Walk in Random Environment
• Behavior of random walk on discrete point processes
• Diffusivity and Ballistic Behavior of Random Walk in Random Environment

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