Heat kernel estimates for strongly recurrent random walk on random media
Probability
2008-08-01 v2 Mathematical Physics
math.MP
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 \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.
Cite
@article{arxiv.0806.4507,
title = {Heat kernel estimates for strongly recurrent random walk on random media},
author = {Takashi Kumagai and Jun Misumi},
journal= {arXiv preprint arXiv:0806.4507},
year = {2008}
}
Comments
24 pages. Journal of Theoretical Probability, to appear