Automatically assigned DDC number: 519282

Manually assigned DDC number: 519282

Number of references: 4

Title: The Intersection Exponent for Simple Random Walk

Author:

Author:

Subject: Gregory F. Lawler,Emily E. Puckette The Intersection Exponent for Simple Random Walk

Description: The intersection exponent 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 Gamma¸ . 1 Introduction The intersection exponent is a measure of the rate of decay of the probability of nonintersection of independent paths of simple random walks. Let S t ; S 1 t ; S 2 t ; Delta Delta Delta be independent simple random walks in Z d (d = 2; 3) starting at the origin. The intersection exponent ¸ = ¸ d (1; k) is defined by the relation PfS[0; n 2 ] " (S 1 (0; n 2 ] [ Delta Delta Delta [ S k (0; n 2 ]) = ;g ß n Gamma¸ : This exponent is only nontrivial for d = 2; 3, and that is why we restrict to those values. If d = 1, the gambler's ruin est...

Contributor: The Pennsylvania State University CiteSeer Archives

Publisher: unknown

Date: 1998-06-25

Pubyear: 1998

Format: ps

Identifier: http://citeseer.ist.psu.edu/140850.html

Source: http://www.math.duke.edu/~jose/walkexp.ps

Language: en

Relation:

Relation:

Relation:

Relation:

Rights: unrestricted

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