On Decay of Correlations for Exclusion Processes with Asymmetric Boundary Conditions

TL;DR

This paper investigates how correlations decay in a symmetric exclusion process with boundary conditions, showing asymptotic independence at large distances using a new probabilistic approach.

Contribution

It introduces a novel recurrent probabilistic method as an alternative to algebraic techniques for analyzing correlation decay.

Findings

Correlations decay asymptotically with distance.

Stationary distribution points become independent at large separations.

New probabilistic approach effectively analyzes boundary-driven exclusion processes.

Abstract

We consider a symmetric exclusion process on a discrete interval of $S$ points with various boundary conditions at the endpoints. We study the asymptotic decay of correlations as $S\to\infty$. The main result is asymptotic independence of a stationary distribution whem the points are far away from each other. We develop a new recurrent probabilistic approach which is an alternative to Derrida's algebraic technique.