Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling

TL;DR

This paper proves that both biased card shuffling and ASEP exhibit cutoff phenomena in their mixing times, using hydrodynamic analysis, eigenfunctions, and concentration inequalities.

Contribution

It establishes the cutoff phenomenon for ASEP and biased card shuffling, providing a detailed asymptotic analysis of their mixing times.

Findings

Both processes display cutoff in mixing times

Hydrodynamic profile analysis is key to understanding cutoff

The methods combine eigenfunction techniques and concentration inequalities

Abstract

We consider the biased card shuffling and the Asymmetric Simple Exclusion Process (ASEP) on the segment. We obtain the asymptotic of their mixing times: our result show that these two continuous-time Markov chains display cutoff. Our analysis combines several ingredients including: a study of the hydrodynamic profile for ASEP, the use of monotonic eigenfunctions, stochastic comparisons and concentration inequalities.