THE MEAN-FIELD ZERO-RANGE PROCESS WITH UNBOUNDED MONOTONE RATES: MIXING TIME, CUTOFF, AND POINCARe CONSTANT

• 成果类型: Article
• 署名作者: Tran, Hong Quan
• 署名单位: Universite PSL; Universite Paris-Dauphine
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1851
• 发表日期: 2023
• 页码: 1732-1757
• 关键词: spectral-gap

摘要

We consider the mean-field zero-range process in the regime where the potential function r is increasing to infinity at sublinear speed, and the den-sity of particles is bounded. We determine the mixing time of the system, and establish cutoff. We also prove that the Poincare constant is bounded away from zero and infinity. This mean-field estimate extends to arbitrary geome-tries via a comparison argument. Our proof uses the path-coupling method of Bubley and Dyer and stochastic calculus.