Preprint C60/2007
On the Central Limit Theorem for a tagged particle in the simple exclusion process

Milton David Jara

**Keywords: **
Tagged particle | simple exclusion | central limit theorem | hydrodynamic limit

We consider the motion of a tagged particle for the simple exclusion process. In equilibrium, for mean-zero simple exclusion processes in any dimension and for asymmetric simple exclusion process in dimension at least 3, we prove that the diffusion coefficient of a tagged particle in infinite volume can be approximated by the diffusion coefficient in growing finite boxes. Out of equilibrium, for the symmetric, nearest-neighbors simple exclusion process in dimension 1, we prove a central limit theorem for the tagged particle in terms of the hydrodynamic equation associated to the process, in this case, the heat equation.