QUENCHED INVARIANCE PRINCIPLES FOR RANDOM WALKS AND ELLIPTIC DIFFUSIONS IN RANDOM MEDIA WITH BOUNDARY

• 成果类型: Article
• 署名作者: Chen, Zhen-Qing; Croydon, David A.; Kumagai, Takashi
• 署名单位: University of Washington; University of Washington Seattle; University of Warwick; Kyoto University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/14-AOP914
• 发表日期: 2015
• 页码: 1594-1642
• 关键词: parabolic harnack inequality; reversible markov-processes; order large deviations; jump-processes; limit-theorem; percolation; homogenization; SEQUENCES; discrete; BEHAVIOR

摘要

Via a Dirichlet form extension theorem and making full use of two-sided heat kernel estimates, we establish quenched invariance principles for random walks in random environments with a boundary. In particular, we prove that the random walk on a supercritical percolation cluster or among random conductances bounded uniformly from below in a half-space, quarter-space, etc., converges when rescaled diffusively to a reflecting Brownian motion, which has been one of the important open problems in this area. We establish a similar result for the random conductance model in a box, which allows us to improve existing asymptotic estimates for the relevant mixing time. Furthermore, in the uniformly elliptic case, we present quenched invariance principles for domains with more general boundaries.