The disconnection exponent for simple random walk |
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| Authors: | Gregory F Lawler Emily E Puckette |
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| Institution: | (1) Department of Mathematics, Duke University, Box 90320, 27708-0320 Durham, NC, USA;(2) Department of Mathematics, Occidental College, 90041 Los Angeles, CA, USA |
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| Abstract: | LetS(t) denote a simple random walk inZ
2 with integer timet. The disconnection exponent
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
. 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. |
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