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

Details The volume and time comparison principle and transition probability estimates for random walks The volume and time comparison principle and transition probability estimates for random walks

2008-01-15

arxiv.org/abs/0801.2393v1

Discrete Random Walks, DRW'03, Conference Volume AC (2003), pp. 301-308,Cyril Banderier and Christian Krattenthaler (eds.)

Mathematics

Probability

Scientific paper

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.

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