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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43}

**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