The probability that planar loop-erased random walk uses a given edge
Probability
2013-01-24 v1
Abstract
We give a new proof of a result of Rick Kenyon that the probability that an edge in the middle of an n x n square is used in a loop-erased walk connecting opposites sides is of order n^{-3/4}. We, in fact, improve the result by showing that this estimate is correct up to multiplicative constants.
Keywords
Cite
@article{arxiv.1301.5331,
title = {The probability that planar loop-erased random walk uses a given edge},
author = {Gregory F. Lawler},
journal= {arXiv preprint arXiv:1301.5331},
year = {2013}
}