Coupling hydrodynamics of several Facilitated Exclusion Processes with closed boundaries

TL;DR

This paper establishes the hydrodynamic limits of the Facilitated Exclusion Process with closed boundaries across various regimes by coupling it with the well-understood Simple Exclusion Process.

Contribution

It introduces a coupling method that transforms facilitated dynamics into simple exclusion dynamics, enabling the derivation of hydrodynamic limits for the facilitated process.

Findings

Hydrodynamic limits are proven for symmetric, asymmetric, and weakly asymmetric regimes.

The coupling with the simple exclusion process simplifies the analysis.

Hydrodynamic behavior matches that of the simple exclusion process with closed boundaries.

Abstract

In this paper, we prove the hydrodynamic limit for the ergodic dynamics of the Facilitated Exclusion Process with closed boundaries in the symmetric, asymmetric and weakly asymmetric regimes. For this, we couple it with a Simple Exclusion Process by constructing a mapping that transforms the facilitated dynamics into the simple one. As the hydrodynamic behaviour of the simple exclusion process with closed boundaries has been extensively studied, we can deduce the corresponding hydrodynamics for the facilitated exclusion process.