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2005 Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk
Michael Kozdron, Gregory Lawler
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Electron. J. Probab. 10: 1442-1467 (2005). DOI: 10.1214/EJP.v10-294

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.

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Michael Kozdron. Gregory Lawler. "Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk." Electron. J. Probab. 10 1442 - 1467, 2005. https://doi.org/10.1214/EJP.v10-294

Information

Accepted: 19 December 2005; Published: 2005
First available in Project Euclid: 1 June 2016

zbMATH: 1110.60046
MathSciNet: MR2191635
Digital Object Identifier: 10.1214/EJP.v10-294

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