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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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