Estimates of random walk exit probabilities and application to loop-erased random walk
Probability
2009-05-15 v1
Abstract
We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z^2 starting on the boundary exits A at another specified boundary point. The estimates are uniform over all domains of a given inradius. We apply these estimates to prove a conjecture of S. Fomin in 2001 concerning a relationship between crossing probabilities of loop-erased random walk and Brownian motion.
Cite
@article{arxiv.math/0501189,
title = {Estimates of random walk exit probabilities and application to loop-erased random walk},
author = {Michael J. Kozdron and Gregory F. Lawler},
journal= {arXiv preprint arXiv:math/0501189},
year = {2009}
}
Comments
26 pages, 0 figures