Cutoff phenomenon for asymmetric zero range process with monotone rates

2024/10/07 by Rameh, Ons
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2410.05220

Abstract

We investigate the mixing time of the asymmetric Zero Range process on the segment with a non-decreasing rate. We show that the cutoff holds in the totally asymmetric case with a convex flux, and also with a concave flux if the asymmetry is strong enough. We show that the mixing occurs when the macroscopic system reaches equilibrium. A key ingredient of the proof, of independent interest, is the hydrodynamic limit for irregular initial data.

Related

• Cutoff for the mean-field zero-range process with bounded monotone rates
• Cutoff for the mean-field zero-range process
• Mixing time and cutoff for one dimensional particle systems
• The mean-field Zero-Range process with unbounded monotone rates: mixing time, cutoff, and Poincaré constant
• Mixing time and cutoff for the weakly asymmetric simple exclusion process