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

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 α∕n or (1−α)∕n (resp. β∕n or (1−β)∕n) where α,β>0 and n is a scaling parameter. We obtain the non-equilibrium fluctuations and from the latter we obtain also the non-equilibrium stationary fluctuations.