The volume and time comparison principle and transition probability estimates for random walks
Probability
2008-01-17 v1
Abstract
This paper presents necessary and sufficient conditions for on- and off-diagonal transition probability estimates for random walks on weighted graphs. On the integer lattice and on may fractal type graphs both the volume of a ball and the mean exit time from a ball is independent of the centre, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is given if uniformity in the space assumed only for the mean exit time.
Cite
@article{arxiv.0801.2393,
title = {The volume and time comparison principle and transition probability estimates for random walks},
author = {Andras Telcs},
journal= {arXiv preprint arXiv:0801.2393},
year = {2008}
}