SCALING LIMITS FOR SUB-BALLISTIC BIASED RANDOM WALKS IN RANDOM CONDUCTANCES

• 成果类型: Article
• 署名作者: Fribergh, Alexander; Kious, Daniel
• 署名单位: Universite de Montreal; New York University; NYU Shanghai
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/16-AOP1159
• 发表日期: 2018
• 页码: 605-686
• 关键词: quenched invariance-principles; percolation; CONVERGENCE; DIFFUSIONS; DYNAMICS; speed

摘要

We consider biased random walks in positive random conductances on the d-dimensional lattice in the zero-speed regime and study their scaling limits. We obtain a functional law of large numbers for the position of the walker, properly rescaled. Moreover, we state a functional central limit theorem where an atypical process, related to the fractional kinetics, appears in the limit.