HIDDEN SYMMETRIES AND LIMIT LAWS IN THE EXTREME ORDER STATISTICS OF THE LAPLACE RANDOM WALK

• 成果类型: Article
• 署名作者: Pitman, Jim; Tang, Wenpin
• 署名单位: University of California System; University of California Berkeley; Columbia University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/22-AOP1572
• 发表日期: 2022
• 页码: 1647-1673
• 关键词: branching-processes; Local Time; DECOMPOSITION; excursions

摘要

This paper is concerned with the limit laws of the extreme order statistics derived from a symmetric Laplace walk. We provide two different descriptions of the point process of the limiting extreme order statistics: a branching representation and a squared Bessel representation. These complementary descriptions expose various hidden symmetries in branching processes and Brownian motion which lie behind some striking formulas found by Schehr and Majumdar (Phys. Rev. Lett. 108 (2012) 040601). In particular, the Bessel process of dimension 4 = 2 + 2 appears in the descriptions as a path decomposition of Brownian motion at a local minimum and the Ray-Knight description of Brownian local times near the minimum.