Random walks among time increasing conductances: heat kernel estimates

• 成果类型: Article
• 署名作者: Dembo, Amir; Huang, Ruojun; Zheng, Tianyi
• 署名单位: Stanford University; Stanford University; University of California System; University of California San Diego
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-018-0894-1
• 发表日期: 2019
• 页码: 397-445
• 关键词: parabolic harnack inequality; local dirichlet spaces; finite markov-chains; bounds; nash

摘要

For any graph having a suitable uniform Poincare inequality and volume growth regularity, we establish two-sided Gaussian transition density estimates and parabolic Harnack inequality, for constant speed continuous time random walks evolving via time varying, uniformly elliptic conductances, provided the vertex conductances (i.e. reversing measures), increase in time. Such transition density upper bounds apply for discrete time uniformly lazy walks, with the matching lower bounds holding once the parabolic Harnack inequality is proved.