DRIVEN TRACER PARTICLE IN ONE-DIMENSIONAL SYMMETRICAL SIMPLE EXCLUSION

Consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard core interactio n. We investigate the behavior of a tagged particle under the action o f an external constant driving force. We prove that the diffusively re scaled position of the test particle epsilon X(epsilon(-2)t), t > 0, c onverges in probability, as epsilon --> 0, to a deterministic function v(t). The function v(.) depends on the initial distribution of the ra ndom environment through a non-linear parabolic equation. This law of large numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional symmetric zero range process with an asymmetry at the origin, An Einstein relat ion is satisfied asymptotically when the external force is small.