Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances

16 Jan 2019  ·  Andres Sebastian, Deuschel Jean-Dominique, Slowik Martin ·

We establish heat kernel upper bounds for a continuous-time random walk under unbounded conductances satisfying an integrability assumption, where we correct and extend recent results by the authors to a general class of speed measures. The resulting heat kernel estimates are governed by the intrinsic metric induced by the speed measure... We also provide a comparison result of this metric with the usual graph distance, which is optimal in the context of the random conductance model with ergodic conductances. read more

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Probability Analysis of PDEs