EINSTEIN RELATION FOR RANDOM WALKS IN RANDOM ENVIRONMENT

• 成果类型: Article
• 署名作者: Guo, Xiaoqin
• 署名单位: Technical University of Munich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP975
• 发表日期: 2016
• 页码: 324-359
• 关键词: ballistic random-walks; large numbers; DIFFUSIONS; LAW

摘要

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.