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The disconnection exponent for simple random walk
Authors:Gregory F. Lawler  Emily E. Puckette
Affiliation:(1) Department of Mathematics, Duke University, Box 90320, 27708-0320 Durham, NC, USA;(2) Department of Mathematics, Occidental College, 90041 Los Angeles, CA, USA
Abstract:LetS(t) denote a simple random walk inZ 2 with integer timet. The disconnection exponent 
$$bar gamma $$
is defined by saying the probability that the path ofS starting at 0 and ending at the circle of radiusn disconnects 0 from infinity decays like 
$$n^{ - bar gamma } $$
. We prove that the disconnection exponent is well-defined and equals the disconnection exponent for Brownian motion which is known to exist. Research supported by the National Science Foundation.
Keywords:
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