The Annals of Probability

What is the probability of intersecting the set of Brownian double points?

Robin Pemantle and Yuval Peres

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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.

Article information

Ann. Probab., Volume 35, Number 6 (2007), 2044-2062.

First available in Project Euclid: 8 October 2007

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Zentralblatt MATH identifier

Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]

Capacity polar decomposition multiparameter Brownian motion regular point


Pemantle, Robin; Peres, Yuval. What is the probability of intersecting the set of Brownian double points?. Ann. Probab. 35 (2007), no. 6, 2044--2062. doi:10.1214/009117907000000169.

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