The Annals of Probability
- Ann. Probab.
- Volume 35, Number 6 (2007), 2044-2062.
What is the probability of intersecting the set of Brownian double points?
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.
Ann. Probab., Volume 35, Number 6 (2007), 2044-2062.
First available in Project Euclid: 8 October 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60J45: Probabilistic potential theory [See also 31Cxx, 31D05]
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. https://projecteuclid.org/euclid.aop/1191860415