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

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

2009-12-24

arxiv.org/abs/0912.4765v1

Mathematics

Probability

37 pages

Scientific paper

We study simple random walk on the uniform spanning tree on Z^2 . 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 Z^2 is 16/13 almost surely.

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