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January 2016 Einstein relation for random walks in random environment
Xiaoqin Guo
Ann. Probab. 44(1): 324-359 (January 2016). DOI: 10.1214/14-AOP975


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.


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Xiaoqin Guo. "Einstein relation for random walks in random environment." Ann. Probab. 44 (1) 324 - 359, January 2016.


Received: 1 October 2013; Revised: 1 July 2014; Published: January 2016
First available in Project Euclid: 2 February 2016

zbMATH: 1339.60142
MathSciNet: MR3456340
Digital Object Identifier: 10.1214/14-AOP975

Primary: 60K37

Keywords: Einstein relation , perturbation , random environment , Random walks , velocity

Rights: Copyright © 2016 Institute of Mathematical Statistics


Vol.44 • No. 1 • January 2016
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