Gradient estimates of the heat kernel for random walks among time-dependent random conductances
Abstract
Abstract In this paper we consider a time-continuous random walk in $$\mathbb {Z}^{d}$$ 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].
Fields of Study & Subjects
Stochastic processes and statistical mechanics
Diffusion and Search Dynamics
Markov Chains and Monte Carlo Methods
Publication details
- Journal / source
- Probability Theory and Related Fields
- Publisher
- Springer Science and Business Media LLC
- Volume
- 195
- Issue
- 3-4
- Pages
- 871–920
- Publication date
- 22 May 2026
- Language
- EN