The volume and time comparison principle and transition probability estimates for random walksArticle

Authors: András Telcs ^{1}

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András Telcs

1 Department of Computer Science [Budapest]

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 are independent of the center, uniform in space. Here the upper estimate is given without such restriction and two-sided estimate is given if the mean exit time is independent of the center but the volume is not.