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

• 成果类型: Article
• 署名作者: Pemantle, Robin; Peres, Yuval
• 署名单位: University of Pennsylvania; University of California System; University of California Berkeley
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117907000000169
• 发表日期: 2007
• 页码: 2044-2062
• 关键词: capacity

摘要

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.