Einstein relation for reversible random walks in random environment on Z

Hoang-Chuong Lam and Jerome Depauw

Stochastic Processes and their Applications, 2016, vol. 126, issue 4, 983-996

Abstract: The aim of this paper is to consider reversible random walk in a random environment in one dimension and prove the Einstein relation for this model. It says that the derivative at 0 of the effective velocity under an additional local drift equals the diffusivity of the model without drift (Theorem 1.2). Our method here is very simple: we solve the Poisson equation (Pω−I)g=f and then use the pointwise ergodic theorem in Wiener (1939) [10] to treat the limit of the solutions to obtain the desired result. There are analogous results for Markov processes with discrete space and for diffusions in random environment.

Keywords: Einstein relation; Random walk; Random environment (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1016/j.spa.2015.10.007

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