Invariant measures for the strong-facilitated exclusion process

Abstract

Consider a generalized model of the facilitated exclusion process, which is a one-dimensional exclusion process with a dynamical constraint that prevents the particle at site x from jumping to x + 1 (or x − 1) if the sites x − 1, x − 2 (or x + 1, x + 2) are empty. It is non-gradient and lacks invariant measures of product form. The purpose of this paper is to identify the invariant measures and to show that they satisfy both exponential decay of correlations and equivalence of ensembles. These properties will play a pivotal role in deriving the hydrodynamic limit.