Equilibrium fluctuations of asymmetric simple exclusion processes in dimension d≥3

We consider an asymmetric exclusion process in dimension d ≥ 3 under diffusive rescaling starting from the Bernoulli product measure with density 0 < α < 1. We prove that the density fluctuation field YNt converges to a generalized Ornstein-Uhlenbeck process, which is formally the solution of the stochastic differential equation dYt = Script A signYtdt + dB∇t, where Script A sign is a second order differential operator and B∇t is a mean zero Gaussian field with known covariances.