Fluctuations for a ∇φ interface model with repulsion from a wall

Abstract

We consider a ∇φ interface model on a one-dimensional lattice with repulsion from a hard wall. We suppose that the repulsion is of the form cφ−α−1, where c,α>0 and φ denotes the height of the interface from the wall. We prove convergence of the equilibrium fluctuations around the hydrodynamic limit to the solution of a SPDE with singular drift. If c→0 the system becomes the Funaki-Olla ∇φ interface model with reflection at the wall, whose equilibrium fluctuations converge to the solution of a SPDE with reflection. We give a new proof of this result using the characterization of such solution as the diffusion generated by an infinite dimensional Dirichlet Form, obtained in a previous paper. Our method is based on a study of integration by parts formulae w.r.t. the equilibrium measure of the interface model and allows to avoid the proof of the so called Boltzmann-Gibbs principle. We also obtain convergence of finite dimensional distributions of non-equilibrium fluctuations around the stationary hydrodynamic limit 0.