Stationary states of boundary driven exclusion processes with nonreversible boundary dynamics

TL;DR

This paper establishes a law of large numbers for the empirical density in boundary-driven symmetric exclusion processes with non-reversible boundary dynamics, using duality techniques.

Contribution

It introduces a rigorous proof of a law of large numbers for such processes with non-reversible boundary conditions, expanding understanding of boundary-driven exclusion models.

Findings

Law of large numbers proven for empirical density

Applicable to processes with non-reversible boundary dynamics

Uses duality techniques for proof

Abstract

We prove a law of large numbers for the empirical density of one-dimensional, boundary driven, symmetric exclusion processes with different types of non-reversible dynamics at the boundary. The proofs rely on duality techniques.