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

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.

50 pages

References in corpus (3)

• The cutoff profile for the simple exclusion process on the circle
• Weakly asymmetric bridges and the KPZ equation
• Mixing of the exclusion process with small bias

Cited by in corpus (14)

• Mixing times and cutoffs in open quadratic fermionic systems
• Fastest local entanglement scrambler, multistage thermalization, and a non-Hermitian phantom
• A central limit theorem for descents of a Mallows permutation and its inverse
• The cutoff phenomenon in total variation for nonlinear Langevin systems with small layered stable noise
• Approximating the stationary distribution of the ASEP with open boundaries
• Cutoff profile of the Metropolis biased card shuffling
• Mixing of the Averaging process and its discrete dual on finite-dimensional geometries
• Mixing times and cutoff for the TASEP in the high and low density phase
• Ergodicity bounds for stable Ornstein-Uhlenbeck systems in Wasserstein distance with applications to cutoff stability
• The cutoff phenomenon for the stochastic heat and the wave equation subject to small Lévy noise
• Cutoff thermalization for Ornstein-Uhlenbeck systems with small Lévy noise in the Wasserstein distance
• Mixing time for the asymmetric simple exclusion process in a random environment
• Cutoff ergodicity bounds in Wasserstein distance for a viscous energy shell model with Lévy noise
• The mixing time of the lozenge tiling Glauber dynamics