A quenched invariance principle for non-elliptic random walk in i.i.d. balanced random environment

• 成果类型: Article
• 署名作者: Berger, Noam; Deuschel, Jean-Dominique
• 署名单位: Hebrew University of Jerusalem; Technical University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0478-4
• 发表日期: 2014
• 页码: 91-126
• 关键词: reversible markov-processes; central-limit-theorem; percolation

摘要

We consider a random walk on , in an i.i.d. balanced random environment, that is a random walk for which the probability to jump from to nearest neighbor is the same as to nearest neighbor . Assuming that the environment is genuinely -dimensional and balanced we show a quenched invariance principle: for almost every environment, the diffusively rescaled random walk converges to a Brownian motion with deterministic non-degenerate diffusion matrix. Within the i.i.d. setting, our result extend both Lawler's uniformly elliptic result (Comm Math Phys, 87(1), pp 81-87, 1982/1983) and Guo and Zeitouni's elliptic result (to appear in PTRF, 2010) to the general (non elliptic) case. Our proof is based on analytic methods and percolation arguments.