Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

From dynamic to static large deviations in boundary driven exclusion particle systems


Code(s) de Classification MSC:

Résumé: We consider the large deviations for the stationary measures associated to a boundary driven symmetric simple exclusion process. Starting from the large deviations for the hydrodynamics and following the Freidlin and Wentzell's strategy, we prove that the rate function is given by the quasi--potential of the Freidlin and Wentzell theory. This result is motivated by the recent developments on the non-equilibrium stationary measures by Derrida, Lebowitz and Speer (Large Deviation of the Density Profile in the Steady State of the Open Symmetric Simple Exclusion Process, J. Statist. Phys. 107 (2002), 599--634) and the more closely related dynamical approach by Bertini, De Sole, Gabrielli, Jona Lasinio, Landim (Macroscopic Fluctuation Theory for Stationary Non-Equilibrium States, J. Statist. Phys. 107 (2002), 635--675)

Mots Clés: Particle systems ; Exclusion process ; Open systems ; Steady states ; Large Deviations ; Hydrodynamic limit ; Freidlin-Wentzell approach

Date: 2002-12-18

Prépublication numéro: PMA-781

Pdf file : PMA-781.pdf