Cutoff for the non reversible SSEP with reservoirs

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 [8]. Our result covers the regime $p\ne q$, where the process is not reversible and the invariant probability distribution is not a product measure. In particular, our proof does not require the explicit formula for the invariant measure given by Derrida et al. 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.