Geodesic
Large deviations of the empirical current in interacting particle systems
Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 144-170

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We study current fluctuations in lattice gases in the hydrodynamic scaling limit. More precisely, we prove a large deviation principle for the empirical current in the symmetric simple exclusion process with rate functional $I$. We then estimate the asymptotic probability of a fluctuation of the average current over a large time interval and show that the corresponding rate function can be obtained by solving a variational problem for the functional $I$. For the symmetric simple exclusion process the minimizer is time independent so that this variational problem can be reduced to a time-independent one. On the other hand, for other models the minimizer is time dependent. This phenomenon is naturally interpreted as a dynamical phase transition.
Keywords: interacting particle systems, large deviations
Mots-clés : hydrodynamic limit. 
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     title = {Large deviations of the empirical current in interacting particle systems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {2006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a10/}
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L. Bertini; D. Gabrielli; G. Jona-Lasinio; C. Landim; A. De Sole. Large deviations of the empirical current in interacting particle systems. Teoriâ veroâtnostej i ee primeneniâ, Tome 51 (2006) no. 1, pp. 144-170. http://geodesic.mathdoc.fr/item/TVP_2006_51_1_a10/