Electronic Communications in Probability

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

Sebastian Andres, Jean-Dominique Deuschel, and 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 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.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 5, 17 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1549357292

Digital Object Identifier
doi:10.1214/18-ECP207

Subjects
Primary: 39A12: Discrete version of topics in analysis 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07] 60K37: Processes in random environments 82C41: Dynamics of random walks, random surfaces, lattice animals, etc. [See also 60G50]

Keywords
random walk heat kernel intrinsic metric

Rights
Creative Commons Attribution 4.0 International License.

Citation

Andres, Sebastian; Deuschel, Jean-Dominique; Slowik, Martin. Heat kernel estimates and intrinsic metric for random walks with general speed measure under degenerate conductances. Electron. Commun. Probab. 24 (2019), paper no. 5, 17 pp. doi:10.1214/18-ECP207. https://projecteuclid.org/euclid.ecp/1549357292


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References

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