English

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.

Keywords

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

R2 v1 2026-07-22T17:14:26.883Z