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Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk (2005)

Kozdron, Michael J.; University Of Regina, Canada; Kozdron@math.uregina.ca,
Lawler, Gregory F.; Cornell University, USA; Lawler@math.cornell.edu

Abstract

We prove an estimate for the probability that a simple random walk in a simply connected subset A of Z2 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.

Publication details

Publisher	Institute of Mathematical Statistics
Repository	Electronic Journal of Probability (United States)
Coverage	; ;