Cutoff phenomenon for asymmetric zero range process with monotone rates
Probability
2024-10-08 v1
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.
Cite
@article{arxiv.2410.05220,
title = {Cutoff phenomenon for asymmetric zero range process with monotone rates},
author = {Ons Rameh},
journal= {arXiv preprint arXiv:2410.05220},
year = {2024}
}