The mean-field Zero-Range process with unbounded monotone rates: mixing time, cutoff, and Poincaré constant

2021/04/21 by Hong-Quan Tran, Tran, Hong-Quan
Economics, Econometrics and Finance · Mathematics · #37A25 #60J27 #60K35 #82C22 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2104.10478

openalex publication_date 2021/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 density of particles is bounded. We determine the mixing time of the system, and establish cutoff. We also prove that the Poincaré constant is bounded away from zero and infinity. This mean-field estimate extends to arbitrary geometries via a comparison argument. Our proof uses the path-coupling method of Bubley and Dyer and stochastic calculus.

Related

• Cutoff for the mean-field zero-range process with bounded monotone rates
• Cutoff for the mean-field zero-range process
• Cutoff phenomenon for asymmetric zero range process with monotone rates
• Mixing time and cutoff for one dimensional particle systems
• Mean field limits of a class of conservative systems with position-dependent transition rates