Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs
Probability
2007-05-23 v2
Abstract
Let x and y be chosen uniformly in a graph G. We find the limiting distribution of the length of a loop-erased random walk from x to y on a large class of graphs that include the discrete torus in dimensions 5 and above. Moreover, on this family of graphs we show that a suitably normalized finite-dimensional scaling limit of the uniform spanning tree is a Brownian continuum random tree.
Cite
@article{arxiv.math/0410430,
title = {Scaling limits of the uniform spanning tree and loop-erased random walk on finite graphs},
author = {Yuval Peres and David Revelle},
journal= {arXiv preprint arXiv:math/0410430},
year = {2007}
}
Comments
6/6/05 version is substantially reorganized, with the main proof being more clearly presented as a proof by induction and the individual lemmas are now more self-contained