Einstein relation for reversible random walks in random environment on

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• 作者：Hoang-Chuong Lam^a ; ^b ; ^{lhchuong@ctu.edu.vn" class="auth_mail" title="E-mail the corresponding author} ; Jerome Depauw^c ; ^{jerome.depauw@univ-tours.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：60J15 ; 60F05 ; 60J27
• 刊名：Stochastic Processes and their Applications
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：126
• 期：4
• 页码：983-996
• 全文大小：229 K

文摘

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 0iner hidden">$0$ 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_ω&minus;I)g=finer hidden">$(P_{\omega }\&m<font\; color="red">in</font>us;I)g=f$ 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.