HARMONIC MEASURE IN A MULTIDIMENSIONAL GAMBLER'S PROBLEM

• 成果类型: Article
• 署名作者: Denisov, Denis; Wachtel, Vitali
• 署名单位: University of Manchester; University of Bielefeld
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/24-AAP2069
• 发表日期: 2024
• 页码: 4387-4407
• 关键词: random-walks; Brownian motions

摘要

We consider a random walk in a truncated cone KN, which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study the behaviour of the Green function in this truncated cone as N increases. Using these results we also obtain the asymptotic behaviour of the harmonic The obtained results are applied to a multidimensional gambler's problem studied by Diaconis and Ethier (Staist. Sci. 37 (2022) 289-305). In particular we confirm their conjecture that the probability of eliminating players in a particular order has the same exact asymptotic behaviour as for the Brownian motion approximation. We also provide a rate of convergence of this probability towards this approximation.