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Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media

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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.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Takashi Kumagai

  2. Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan

    Jun Misumi

Authors
  1. Takashi Kumagai
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  2. Jun Misumi
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Correspondence to Takashi Kumagai.

Additional information

T. Kumagai research partially supported by the Grant-in-Aid for Scientific Research (B) 18340027.

J. Misumi research partially supported by the 21 century COE program at Graduate School of Mathematical Sciences, the University of Tokyo.

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Kumagai, T., Misumi, J. Heat Kernel Estimates for Strongly Recurrent Random Walk on Random Media. J Theor Probab 21, 910–935 (2008). https://doi.org/10.1007/s10959-008-0183-5

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  • DOI: https://doi.org/10.1007/s10959-008-0183-5

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