Quenched invariance principles for the random conductance model on a random graph with degenerate ergodic weights

• 成果类型: Article
• 署名作者: Deuschel, Jean-Dominique; Tuan Anh Nguyen; Slowik, Martin
• 署名单位: Technical University of Berlin
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-017-0759-z
• 发表日期: 2018
• 页码: 363-386
• 关键词: reversible markov-processes; random-walks; percolation

摘要

We consider a stationary and ergodic random field that is parameterized by the edge set of the Euclidean lattice , . The random variable , taking values in and satisfying certain moment bounds, is thought of as the conductance of the edge e. Assuming that the set of edges with positive conductances give rise to a unique infinite cluster , we prove a quenched invariance principle for the continuous-time random walk among random conductances under certain moment conditions. An essential ingredient of our proof is a new anchored relative isoperimetric inequality.