Open Access
November 2007 What is the probability of intersecting the set of Brownian double points?
Robin Pemantle, Yuval Peres
Ann. Probab. 35(6): 2044-2062 (November 2007). DOI: 10.1214/009117907000000169


We give potential theoretic estimates for the probability that a set A contains a double point of planar Brownian motion run for unit time. Unlike the probability for A to intersect the range of a Markov process, this cannot be estimated by a capacity of the set A. Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decomposition of A into a set that never intersects the set of Brownian double points and a set for which intersection with the set of Brownian double points is the same as intersection with the Brownian path.


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Robin Pemantle. Yuval Peres. "What is the probability of intersecting the set of Brownian double points?." Ann. Probab. 35 (6) 2044 - 2062, November 2007.


Published: November 2007
First available in Project Euclid: 8 October 2007

zbMATH: 1131.60071
MathSciNet: MR2353382
Digital Object Identifier: 10.1214/009117907000000169

Primary: 60J45

Keywords: capacity , multiparameter Brownian motion , polar decomposition , regular point

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 6 • November 2007
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