Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

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 im...

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Veröffentlicht in:Journal of theoretical probability 2008-12, Vol.21 (4), p.910-935
Hauptverfasser: Kumagai, Takashi, Misumi, Jun
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
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Zusammenfassung: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.
ISSN:0894-9840
1572-9230
DOI:10.1007/s10959-008-0183-5