Spectral dimension and random walks on the two dimensional uniform spanning tree
Probability
2009-12-25 v1
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.
Cite
@article{arxiv.0912.4765,
title = {Spectral dimension and random walks on the two dimensional uniform spanning tree},
author = {Martin T. Barlow and Robert Masson},
journal= {arXiv preprint arXiv:0912.4765},
year = {2009}
}
Comments
37 pages