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

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 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.
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András Telcs. The volume and time comparison principle and transition probability estimates for random walks. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.301-308, ⟨10.46298/dmtcs.3334⟩. ⟨hal-01183929⟩

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