Non-equilibrium and stationary fluctuations of a slowed boundary symmetric exclusion

Abstract

We consider a one-dimensional symmetric simple exclusion process in contact with slowed reservoirs: at the left (resp. right) boundary, particles are either created or removed at rates given by $\alpha /n$ or $(1-\alpha )/n$ (resp. $\beta /n$ or $(1-\beta )/n$) where $\alpha ,\beta >0$ and $n$ is a scaling parameter. We obtain the non-equilibrium fluctuations and consequently the non-equilibrium stationary fluctuations.