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Cutoff for the non reversible SSEP with reservoirs

2022/11/26 by Hong-Quan Tran, Tran, Hong-Quan
Mathematics · #37A25 #60J27 #60K35 #82C22 #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2211.14687

openalex publication_date 2022/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Symmetric Simple Exclusion Process (SSEP) on the segment with two reservoirs of densities p, q ∈ (0,1) at the two endpoints. We show that the system exhibits cutoff with a diffusive window, thus confirming a conjecture of Gantert, Nestoridi, and Schmid in \citeGantert2020. In particular, our result covers the regime p ≠ q, where the process is not reversible and there is no known explicit formula for the invariant measure. Our proof exploits the information percolation framework introduced by Lubetzky and Sly, the negative dependence of the system, and an anticoncentration inequality at the conditional level. We believe this approach is applicable to other models.

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