Equilibrium Fluctuations for $\nabla_{\varphi}$ Interface Model

Abstract

We study the large scale space–time fluctuations of an interface which is modeled by a massless scalar field with reversible Langevin dynamics. For a strictly convex interaction potential we prove that on a large space–time scale these fluctuations are governed by an infinite-dimensional Ornstein –Uhlenbeck process. Its effective diffusion type covariance matrix is characterized through a variational formula.