Cutoff for the non reversible SSEP with reservoirs

TL;DR

This paper proves that the non-reversible SSEP with reservoirs exhibits cutoff with a diffusive window, confirming a previous conjecture, even in the non-reversible regime without explicit invariant measures.

Contribution

It establishes cutoff for the non-reversible SSEP with reservoirs using information percolation and negative dependence, extending results to regimes without explicit invariant measures.

Findings

System exhibits cutoff with diffusive window

Confirms conjecture of Gantert, Nestoridi, and Schmid

Applicable approach to other models

Abstract

We consider the Symmetric Simple Exclusion Process (SSEP) on the segment with two reservoirs of densities $p, q \in (0,1)$ 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 \cite{Gantert2020}. In particular, our result covers the regime $p \neq q$, 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.