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

Tran, Hong-Quan

Tran, Hong-Quan (2022), The mean-field Zero-Range process with unbounded monotone rates: mixing time, cutoff, and Poincaré constant. https://basepub.dauphine.psl.eu/handle/123456789/23254

View/Open

meanfield-Tran.pdf (293.2Kb)

Type

Document de travail / Working paper

Date

2022

Series title

Cahier de recherche CEREMADE, Université Paris Dauphine-PSL

Published in

Paris

Metadata

Show full item record

Author(s)

Tran, Hong-Quan
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]

Abstract (EN)

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.