Convergence to fractional kinetics for random walks associated with unbounded conductances

• 成果类型: Article
• 署名作者: Barlow, Martin T.; Cerny, Jiri
• 署名单位: University of British Columbia; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-009-0257-z
• 发表日期: 2011
• 页码: 639-673
• 关键词: quenched invariance-principles; reversible markov-processes; limit-theorem; percolation; diffusion; DYNAMICS; MODEL

摘要

We consider a random walk among unbounded random conductances whose distribution has infinite expectation and polynomial tail. We prove that the scaling limit of this process is a Fractional-Kinetics process-that is the time change of a d-dimensional Brownian motion by the inverse of an independent alpha-stable subordinator. We further show that the same process appears in the scaling limit of the non-symmetric Bouchaud's trap model.