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

Sebastian Andres; Jean-Dominique Deuschel; Martin Slowik

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arXiv · 1711.11119

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

Sebastian Andres·Jean-Dominique Deuschel·Martin Slowik

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Abstract

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.

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BibTeX RIS

Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik. 2019-01-16. Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances. https://arxiv.org/abs/1711.11119

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