On Decay of Correlations for Exclusion Processes with Asymmetric Boundary Conditions

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 $S\to \mathrm{\infty }$. 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.