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Abstract

We consider the one-dimensional weakly asymmetric nearest neighbour exclusion process and study, in macroscopic space-time coordinates, the fluctuations of the associated density field around the solution of the nonlinear BURGERS equation with viscosity. We show that this fluctuations converge to a generalized ORNSTEIN-UHLENBECK process, the drift term of which can be obtained by linearization of the BURGERS equation. Our approach is based on a nonlinear transformation of the exclusion process.