THE BEURLING ESTIMATE FOR A CLASS OF RANDOM WALKS
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Gregory F. Lawler and Vlada Limic
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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 $-\epsilon$ reaches the unit circle 
without hitting the curve is bounded above by $ c \, \epsilon^{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. We extend this estimate to random walks with zero mean and finite $(3+\delta)-$moment.