Mixing times and cutoff for the TASEP in the high and low density phase

Abstract

We study the totally asymmetric simple exclusion process with open boundaries in the high density and the low density phase. In the bulk of the two phases, we show that the process on a segment of length $N$ exhibits cutoff at order $N$, while in the intersection of the phases, the coexistence line, the mixing time is of order $N^2$, and no cutoff occurs. In particular, we determine the $\epsilon$-mixing time in the coexistence line up to constant factors, which do not dependent on $\epsilon$. Combined with previous results on the maximal current phase, this completes the picture on mixing times for the TASEP with open boundaries.

arXiv comment43 pages, 8 figures, substantially revised

References in corpus (18)

• Mixing times of lozenge tiling and card shuffling Markov chains
• Exact Spectral Gaps of the Asymmetric Exclusion Process with Open Boundaries
• Asymmetric Simple Exclusion Process with Open Boundaries and Askey-Wilson Polynomials
• The cutoff profile for the simple exclusion process on the circle
• Mixing time and cutoff for the adjacent transposition shuffle and the simple exclusion
• Pfaffian Schur processes and last passage percolation in a half-quadrant
• Density Profile of the One-Dimensional Partially Asymmetric Simple Exclusion Process with Open Boundaries
• Mixing of the symmetric exclusion processes in terms of the corresponding single-particle random walk
• Cutoff phenomenon for the asymmetric simple exclusion process and the biased card shuffling
• Non-existence of bi-infinite geodesics in the exponential corner growth model
• Correlation Function of Asymmetric Simple Exclusion Process with Open Boundaries
• Stationary half-space last passage percolation
• A reverse duality for the ASEP with open boundaries
• Optimal Exponent for Coalescence of Finite Geodesics in Exponential Last Passage Percolation
• Limit fluctuations for density of asymmetric simple exclusion processes with open boundaries
• A Determinantal Formula for Catalan Tableaux and TASEP Probabilities
• Mixing times for the simple exclusion process in ballistic random environment
• Moderate deviation and exit time estimates for stationary Last Passage Percolation

Cited by in corpus (2)

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