Cutoff phenomenon for asymmetric zero range process with monotone rates

Ons Rameh

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arXiv · 2410.05220

Cutoff phenomenon for asymmetric zero range process with monotone rates

Ons Rameh

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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.

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Ons Rameh. 2024-10-07. Cutoff phenomenon for asymmetric zero range process with monotone rates. https://arxiv.org/abs/2410.05220

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