%0 Journal Article
%T The volume and time comparison principle and transition probability estimates for random walks
%A Andras Telcs
%J Mathematics
%D 2008
%I arXiv
%X 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.
%U http://arxiv.org/abs/0801.2393v1