Quenched local central limit theorem for random walks in a time-dependent balanced random environment

• 成果类型: Article
• 署名作者: Deuschel, Jean-Dominique; Guo, Xiaoqin
• 署名单位: Technical University of Berlin; University of Wisconsin System; University of Wisconsin Madison; University System of Ohio; University of Cincinnati
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01097-7
• 发表日期: 2022
• 页码: 111-156
• 关键词: 2nd-order parabolic equations; invariance-principle; difference-operators; harnack inequality; positive solutions; BOUNDARY; form

摘要

We prove a quenched local central limit theorem for continuous-time random walks in Z(d), d >= 2, in a uniformly-elliptic time-dependent balanced random environment which is ergodic under space-time shifts. We also obtain Gaussian upper and lower bounds for quenched and (positive and negative) moment estimates of the transition probabilities and asymptotics of the discrete Green's function.