Equilibrium Fluctuations for Interacting Ornstein-Uhlenbeck Particles

Abstract

We study the hydrodynamic density fluctuations of an infinite system of interacting particles on ℝ d . The particles interact between them through a two body superstable potential, and with a surrounding fluid in equilibrium through a random viscous force of Ornstein-Uhlenbeck type. The stationary initial distribution is the Gibbs measure associated with the potential and with a given temperature and fugacity. We prove that the time-dependent density fluctuation field converges in law, under diffusive scaling of space and time, to the solution of a linear stochastic partial differential equation driven by white noise.