Electronic Communications in Probability

Anomalous heat kernel behaviour for the dynamic random conductance model

Stephen Buckley

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Abstract

We introduce the time dynamic random conductance model and consider the heat kernel for the random walk on this environment. In the case where conductances are bounded above, an example environment is presented which exhibits heat kernel decay that is asymptotically slower than in the well studied time homogeneous case - being close to $O\left( n^{-1}\right) $ as opposed to $O\left( n^{-2}\right) $. The example environment given is a modification of an environment introduced in Berger, Biskup, Hoffman and Kozma (2008).

Article information

Source
Electron. Commun. Probab., Volume 18 (2013), paper no. 1, 11 pp.

Dates
Accepted: 3 January 2013
First available in Project Euclid: 7 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1465315540

Digital Object Identifier
doi:10.1214/ECP.v18-2525

Mathematical Reviews number (MathSciNet)
MR3011528

Zentralblatt MATH identifier
1320.60162

Subjects
Primary: 60G50: Sums of independent random variables; random walks
Secondary: 60J27: Continuous-time Markov processes on discrete state spaces 05C81: Random walks on graphs

Keywords
heat kernel random walk in random environment random conductances

Rights
This work is licensed under a Creative Commons Attribution 3.0 License.

Citation

Buckley, Stephen. Anomalous heat kernel behaviour for the dynamic random conductance model. Electron. Commun. Probab. 18 (2013), paper no. 1, 11 pp. doi:10.1214/ECP.v18-2525. https://projecteuclid.org/euclid.ecp/1465315540


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