Driven Tracer Particle in One Dimensional Symmetric Simple Exclusion |
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Authors: | C Landim S Olla S B Volchan |
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Institution: | IMPA, Estrada Dona Castorina 110, CEP 22460 Rio de Janeiro, Brasil.?E-mail: landim@impa.br, volchan@impa.br, BR Département de Mathéatiques, Université de Cergy-Pontoise, 2 Av. Adolphe Chauvin, Pontoise 95302 Cergy-Pontoise Cedex, France and Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau cedex, France. E-mail: olla@paris.polytechnique.fr, FR
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Abstract: | Consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard
core interaction. We investigate the behavior of a tagged particle under the action of an external constant driving force.
We prove that the diffusively rescaled position of the test particle εX(ε-2
t), t > 0, converges in probability, as ε→ 0, to a deterministic function v(t). The function v(⋅) depends on the initial distribution of the random 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 relation is satisfied asymptotically when the external
force is small.
Received: 5 December 1996 / Accepted: 30 June 1997 |
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