Work

Harmonic measure in a multidimensional gambler’s problem

Year: 2024

Type: article

Abstract: 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 measure. 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.

Source: The Annals of Applied Probability

DOI: 10.1214/24-aap2069

Authors: Denis Denisov, Vitali Wachtel

Institutions: University of Manchester, Bielefeld University

Language: English

Topic: Stochastic processes and statistical mechanics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Leverhulme Trust, Deutsche Forschungsgemeinschaft

Awards: G1288578048, G7992576571, SFB 1283: Unsicherheit beherrschen und Zufall sowie Unordnung nutzen in Analysis, Stochastik und deren Anwendungen