Estimates of random walk exit probabilities and application to loop-erased random walk. (English) Zbl 1110.60046
Summary: 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.
MSC:
| 60G50 | Sums of independent random variables; random walks |
| 60J45 | Probabilistic potential theory |
| 60J65 | Brownian motion |
| 82B41 | Random walks, random surfaces, lattice animals, etc. in equilibrium statistical mechanics |
| 60F99 | Limit theorems in probability theory |
