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Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

Author

Listed:
  • Takashi Kumagai

    (Kyoto University)

  • Jun Misumi

    (The University of Tokyo)

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.

Suggested Citation

  • Takashi Kumagai & Jun Misumi, 2008. "Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media," Journal of Theoretical Probability, Springer, vol. 21(4), pages 910-935, December.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:4:d:10.1007_s10959-008-0183-5
    DOI: 10.1007/s10959-008-0183-5
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    Cited by:

    1. Andres, Sebastian & Croydon, David A. & Kumagai, Takashi, 2024. "Heat kernel fluctuations and quantitative homogenization for the one-dimensional Bouchaud trap model," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    2. Kazuki Okamura, 2021. "Some Results for Range of Random Walk on Graph with Spectral Dimension Two," Journal of Theoretical Probability, Springer, vol. 34(3), pages 1653-1688, September.

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