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

   
@article{EJP294,
	author = {Michael Kozdron and Gregory Lawler},
	title = {Estimates of Random Walk Exit Probabilities and Application to Loop-Erased Random Walk},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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.},
	pages = {no. 44, 1442-1467},
	issn = {1083-6489},
	doi = {10.1214/EJP.v10-294},    
        url = {http://ejp.ejpecp.org/article/view/294}}