Heat kernel estimates for random walks with degenerate weights

Abstract

We establish Gaussian-type upper bounds on the heat kernel for a continuous-time random walk on a graph with unbounded weights under an ergodicity assumption. For the proof we use Davies' perturbation method, where we show a maximal inequality for the perturbed heat kernel via Moser iteration.

24 pages; in this version we corrected statement and proof of Theorem 1.10 and removed a minor technical gap in the iteration argument

References in corpus (3)

• Random walks on supercritical percolation clusters
• Invariance principle for the random conductance model with unbounded conductances
• Anomalous heat-kernel decay for random walk among bounded random conductances

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• First passage percolation with long-range correlations and applications to random Schrödinger operators
• Random walks in random conductances: decoupling and spread of infection
• Homogenization theory of random walks among deterministic conductances