Einstein relation for reversible random walks in random environment on Z

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:126

Article

Lam, Hoang-Chuong^1,2  Depauw, Jerome³ 

[1] Can Tho Univ, Coll Nat Sci, Dept Math, Can Tho City, Vietnam

[2] Ben Gurion Univ Negev, Dept Elect & Comp Engn, POB 653, IL-84105 Beer Sheva, Israel

[3] Univ Tours, Lab Math & Phys Theor, CNRS, UMR 6083, Parc Grandmt, F-37000 Tours, France

关键词: Einstein relation;    Random walk;    Random environment;   

DOI  :  10.1016/j.spa.2015.10.007

来源: Elsevier

【 摘 要 】

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 (P-omega - 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. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free