The Beurling estimate for a class of random walks
Probability
2007-05-23 v1
Abstract
An estimate of Beurling states that if K is a curve from 0 to the unit circle in the complex plane, then the probability that a Brownian motion starting at -eps reaches the unit circle without hitting the curve is bounded above by c eps^{1/2}. This estimate is very useful in analysis of boundary behavior of conformal maps, especially for connected but rough boundaries. The corresponding estimate for simple random walk was first proved by Kesten. In this note we extend this estimate to random walks with zero mean, and finite (3+delta) moment.
Cite
@article{arxiv.math/0403309,
title = {The Beurling estimate for a class of random walks},
author = {Gregory F. Lawler and Vlada Limic},
journal= {arXiv preprint arXiv:math/0403309},
year = {2007}
}
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17 pages