Equilibrium fluctuations for a driven tracer particle dynamics

We study the equilibrium fluctuations of a tagged particle driven by an external constant force in an infinite system of particles evolving in a one-dimensional lattice according to symmetric random walks with exclusion. We prove that when the system is initially in the equilibrium state, the finite-dimensional distributions of the diffusively rescaled position εX(ε−2t) of the tagged particle converges, as ε→0, to the finite-dimensional distributions of a mean zero Gaussian process whose covariance can be expressed in terms of a diffusion process.