Quenched invariance principle for simple random walk on percolation clusters

• 成果类型: Article
• 署名作者: Berger, Noam; Biskup, Marek
• 署名单位: California Institute of Technology; University of California System; University of California Los Angeles
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-006-0498-z
• 发表日期: 2007
• 页码: 83-120
• 关键词: reversible markov-processes; chemical distance; energy; FLOWS

摘要

We consider the simple random walk on the (unique) infinite cluster of supercritical bond percolation in Z(d) with d >= 2. We prove that, for almost every percolation configuration, the path distribution of the walk converges weakly to that of non-degenerate, isotropic Brownian motion. Our analysis is based on the consideration of a harmonic deformation of the infinite cluster on which the random walk becomes a square-integrable martingale. The size of the deformation, expressed by the so called corrector, is estimated by means of ergodicity arguments.