Cutoff for the mixing time of the Facilitated Exclusion Process

TL;DR

This paper determines the mixing time and cutoff phenomena for the Facilitated Exclusion Process by establishing a novel bijective mapping to the symmetric simple exclusion process, revealing new insights into its ergodic and non-ergodic regimes.

Contribution

It introduces a new bijective, deterministic mapping between the FEP and SSEP, enabling precise analysis of mixing times and cutoff phenomena across different regimes.

Findings

Identifies cutoff and pre-cutoff in the FEP.

Establishes a bijective mapping valid in ergodic and non-ergodic regimes.

Provides coupling between tagged particle position and current in SSEP.

Abstract

We compute the mixing time of the Facilitated Exclusion Process (FEP) and obtain cutoff and pre-cutoff in different regimes. The main tool to obtain this result is a new bijective, deterministic mapping between the joint law of an ergodic FEP and its current through the origin, and the joint law of a Symmetric Simple Exclusion Process (SSEP) and its current through the origin. This mapping is interesting in itself, as it remains valid in the non-ergodic regime where it gives a coupling between the position of a tagged particle in the FEP and the current through the origin in a SSEP with traps.