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Heat-kernel estimates for random walk among random conductances with heavy tail

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  • Boukhadra, Omar

Abstract

We study models of discrete-time, symmetric, -valued random walks in random environments, driven by a field of i.i.d. random nearest-neighbor conductances [omega]xy[set membership, variant][0,1], with polynomial tail near 0 with exponent [gamma]>0. We first prove for all d>=5 that the return probability shows an anomalous decay (non-Gaussian) that approaches (up to sub-polynomial terms) a random constant times n-2 when we push the power [gamma] to zero. In contrast, we prove that the heat-kernel decay is as close as we want, in a logarithmic sense, to the standard decay n-d/2 for large values of the parameter [gamma].

Suggested Citation

  • Boukhadra, Omar, 2010. "Heat-kernel estimates for random walk among random conductances with heavy tail," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 182-194, February.
    • Handle: RePEc:eee:spapps:v:120:y:2010:i:2:p:182-194
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    Cited by:

    1. Boukhadra, Omar, 2018. "On heat kernel decay for the random conductance model," Statistics & Probability Letters, Elsevier, vol. 133(C), pages 23-27.

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