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2019 Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances
Sebastian Andres, Jean-Dominique Deuschel, Martin Slowik
Electron. Commun. Probab. 24: 1-17 (2019). DOI: 10.1214/18-ECP207

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 in [3] 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.

Citation

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Sebastian Andres. Jean-Dominique Deuschel. Martin Slowik. "Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances." Electron. Commun. Probab. 24 1 - 17, 2019. https://doi.org/10.1214/18-ECP207

Information

Received: 2 March 2018; Accepted: 22 December 2018; Published: 2019
First available in Project Euclid: 5 February 2019

zbMATH: 1410.82020
MathSciNet: MR3916337
Digital Object Identifier: 10.1214/18-ECP207

Subjects:
Primary: 39A12, 60J35, 60K37, 82C41

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