Nonintersecting Brownian excursions

• 成果类型: Article
• 署名作者: Tracy, Craig A.; Widom, Harold
• 署名单位: University of California System; University of California Davis; University of California System; University of California Santa Cruz
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/105051607000000041
• 发表日期: 2007
• 页码: 953-979
• 关键词: level-spacing distributions; differential-equations; matrices; kernel

摘要

We consider the process of n Brownian excursions conditioned to be nonintersecting. We show the distribution functions for the top curve and the bottom curve are equal to Fredholm determinants whose kernel we give explicitly. In the simplest case, these determinants are expressible in terms of Painleve V functions. We prove that as n -> infinity, the distributional limit of the bottom curve is the Bessel process with parameter 1/2. (This is the Bessel process associated with Dyson's Brownian motion.) We apply these results to study the expected area under the bottom and top curves.