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The Intersection Exponent for Simple Random Walk

Published online by Cambridge University Press:  14 February 2001

GREGORY F. LAWLER  and
EMILY E. PUCKETTE
GREGORY F. LAWLER
Affiliation:
Department of Mathematics, Duke University,Durham, NC 27708-0320, USA (e-mail: [email protected])
EMILY E. PUCKETTE
Affiliation:
Department of Mathematics, Occidental College, Los Angeles, CA 90041-3314, USA (e-mail: [email protected])
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Abstract

The intersection exponent ξ for simple random walk in two and three dimensions gives a measure of the rate of decay of the probability that paths do not intersect. In this paper we show that the intersection exponent for random walks is the same as that for Brownian motion and show in fact that the probability of nonintersection up to distance n is comparable (equal up to multiplicative constants) to n−ξ.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 9 , Issue 5 , September 2000 , pp. 441 - 464
Copyright
2000 Cambridge University Press

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