Discrete fractal dimensions of the ranges of random walks in Zd associate with random conductances

• 成果类型: Article
• 署名作者: Xiao, Yimin; Zheng, Xinghua
• 署名单位: Michigan State University; Hong Kong University of Science & Technology
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-012-0418-3
• 发表日期: 2013
• 页码: 1-26
• 关键词: sample path properties; MODEL

摘要

Let be a continuous time random walk in an environment of i.i.d. random conductances , where E (d) is the set of nonoriented nearest neighbor bonds on the Euclidean lattice and d a parts per thousand yen 3. Let be the range of X. It is proved that, for almost every realization of the environment, dim(H) R = dim(P) R = 2 almost surely, where dim(H) and dim(P) denote, respectively, the discrete Hausdorff and packing dimension. Furthermore, given any set , a criterion for A to be hit by X (t) for arbitrarily large t > 0 is given in terms of dim(H) A. Similar results for Bouchoud's trap model in (d a parts per thousand yen 3) are also proven.