The Annals of Probability

Einstein relation for random walks in random environment

Xiaoqin Guo

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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.

Article information

Source
Ann. Probab., Volume 44, Number 1 (2016), 324-359.

Dates
Received: October 2013
Revised: July 2014
First available in Project Euclid: 2 February 2016

Permanent link to this document
https://projecteuclid.org/euclid.aop/1454423043

Digital Object Identifier
doi:10.1214/14-AOP975

Mathematical Reviews number (MathSciNet)
MR3456340

Zentralblatt MATH identifier
1339.60142

Subjects
Primary: 60K37: Processes in random environments

Keywords
Einstein relation random walks random environment perturbation velocity

Citation

Guo, Xiaoqin. Einstein relation for random walks in random environment. Ann. Probab. 44 (2016), no. 1, 324--359. doi:10.1214/14-AOP975. https://projecteuclid.org/euclid.aop/1454423043


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