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.
Publié le : 2007-11-14
Classification:
Capacity,
polar decomposition,
multiparameter Brownian motion,
regular point,
60J45
@article{1191860415,
author = {Pemantle, Robin and Peres, Yuval},
title = {What is the probability of intersecting the set of Brownian double points?},
journal = {Ann. Probab.},
volume = {35},
number = {1},
year = {2007},
pages = { 2044-2062},
language = {en},
url = {http://dml.mathdoc.fr/item/1191860415}
}
Pemantle, Robin; Peres, Yuval. What is the probability of intersecting the set of Brownian double points?. Ann. Probab., Tome 35 (2007) no. 1, pp. 2044-2062. http://gdmltest.u-ga.fr/item/1191860415/