Spectral dimension and random walks on the two dimensional uniform spanning tree

2009/12/24 by Martin T. Barlow, Barlow, Martin T., Robert Masson +1 · 1 citation
Mathematics · #60G50 #60J10 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60G50 #msc:60J10

paper · pdf · doi:10.48550/arxiv.0912.4765

37 pages

arxiv created 2009/12/24 · arxiv updated 2010/01/14

Abstract

We study simple random walk on the uniform spanning tree on Z² . We obtain estimates for the transition probabilities of the random walk, the distance of the walk from its starting point after n steps, and exit times of both Euclidean balls and balls in the intrinsic graph metric. In particular, we prove that the spectral dimension of the uniform spanning tree on Z² is 16/13 almost surely.

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