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

  • Michael J. Kozdron
We prove an estimate for the probability that a simple random walk in a simply connected subset A ⊂ 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 [4] in 2001 concerning a relationship between crossing… CONTINUE READING