Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

Takashi Kumagai () and Jun Misumi ()
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Takashi Kumagai: Kyoto University
Jun Misumi: The University of Tokyo

Journal of Theoretical Probability, 2008, vol. 21, issue 4, 910-935

Abstract: Abstract We establish general estimates for simple random walk on an arbitrary infinite random graph, assuming suitable bounds on volume and effective resistance for the graph. These are generalizations of the results in Barlow et al. (Commun. Math. Phys. 278:385–431, 2008, Sects. 1, 2) and in particular imply the spectral dimension of the random graph. We will also give an application of the results to random walk on a long-range percolation cluster.

Keywords: Random walk; Random media; Heat kernel estimates; Spectral dimension; Long-range percolation; 60J45; 05C80; 35K05; 82B43 (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10959-008-0183-5

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