The Annals of Probability
- Ann. Probab.
- Volume 44, Number 1 (2016), 324-359.
Einstein relation for random walks in random environment
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.
Ann. Probab., Volume 44, Number 1 (2016), 324-359.
Received: October 2013
Revised: July 2014
First available in Project Euclid: 2 February 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K37: Processes in random environments
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