Gradient estimates of the heat kernel for random walks among time-dependent random conductances

• 成果类型: Article
• 署名作者: Deuschel, Jean-Dominique; Kumagai, Takashi; Slowik, Martin
• 署名单位: Technical University of Berlin; Waseda University; University of Mannheim
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-026-01499-5
• 发表日期: 2026-08
• 页码: 871-920
• 关键词: random conductance model; Time-dependent random environment; Entropy method; heat kernel; invariance-principle; quantitative homogenization; harnack inequality; bounds; MODEL

摘要

In this paper we consider a time-continuous random walk in Z(d) in a dynamical random environment with symmetric jump rates to nearest neighbours. We assume that these random conductances are stationary and ergodic and, moreover, that they are bounded from below but unbounded from above with finite first moment. We derive sharp on-diagonal estimates for the annealed first and second discrete space derivative of the heat kernel which then yield local limit theorems for the corresponding kernels. Assuming weak algebraic off-diagonal estimates, we then extend these results to the annealed Green function and its first and second derivative. Our proof which extends the result of [28] to unbounded conductances with first moment only, is an adaptation of the recent entropy method of [15].