Telcs, András
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The volume and time comparison principle and transition probability estimates for random walks
dmtcs:3334 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2003,
DMTCS Proceedings vol. AC, Discrete Random Walks (DRW'03)
The volume and time comparison principle and transition probability estimates for random walks
Authors: Telcs, András
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.