Heat kernel estimates for strongly recurrent random walk on random media

Details Heat kernel estimates for strongly recurrent random walk on random media Heat kernel estimates for strongly recurrent random walk on random media

2008-06-27

arxiv.org/abs/0806.4507v2

Mathematics

Probability

24 pages. Journal of Theoretical Probability, to appear

Scientific paper

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 \cite[Section 1,2]{BJKS}, 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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