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

Abstract

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.

37 pages

References in corpus (2)

• The Alexander-Orbach conjecture holds in high dimensions
• Exponential tail bounds for loop-erased random walk in two dimensions

Cited by in corpus (1)

• Spectral dimension of trees with a unique infinite spine