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.
Acknowledgments
The author warmly thanks Justin Salez for constructive discussions and his comments on the draft. The author also kindly thanks the anonymous referee for their suggestion to make the paper more clear and readable.
Citation
Hong Quan Tran. "The mean-field zero-range process with unbounded monotone rates: Mixing time, cutoff, and Poincaré constant." Ann. Appl. Probab. 33 (3) 1732 - 1757, June 2023. https://doi.org/10.1214/22-AAP1851
Information