What is the probability of intersecting the set of Brownian double points?
Abstract
We give potential theoretic estimates for the probability that a set contains a double point of planar Brownian motion run for unit time. Unlike the probability for to intersect the range of a Markov process, this cannot be estimated by a capacity of the set . Instead, we introduce the notion of a capacity with respect to two gauge functions simultaneously. We also give a polar decomposition of 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.
Keywords
Cite
@article{arxiv.math/0404105,
title = {What is the probability of intersecting the set of Brownian double points?},
author = {Robin Pemantle and Yuval Peres},
journal= {arXiv preprint arXiv:math/0404105},
year = {2009}
}
Comments
Published in at http://dx.doi.org/10.1214/009117907000000169 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)