  The relaxation towards equilibrium of systems with long range interactions is
not yet fully understood. As a step towards such a comprehension, we propose
the study of the dynamical equilibrium fluctuations in a model system with long
range interaction. We compute analytically, from the microscopic dynamics, the
autocorrelation function of the order parameter. From this result, we derive
analytically a Fokker Planck equation which describes the stochastic process of
the impulsion of a single particle in an equilibrium bath. The diffusion
coefficient is explicitly computed.

Statistical Mechanics