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.

Large deviations of the empirical current in interacting particle systems / Bertini, L; DE SOLE, Alberto; Gabrielli, D; JONA LASINIO, G; Landim, C.. - In: THEORY OF PROBABILITY AND ITS APPLICATIONS. - ISSN 0040-585X. - STAMPA. - 51:1(2006), pp. 2-27. [10.1137/S0040585X97982256]

Large deviations of the empirical current in interacting particle systems

BERTINI L;DE SOLE, ALBERTO;
2006

Abstract

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.
2006
interacting particle systems; large deviations; hydrodynamic limit
01 Pubblicazione su rivista::01a Articolo in rivista
Large deviations of the empirical current in interacting particle systems / Bertini, L; DE SOLE, Alberto; Gabrielli, D; JONA LASINIO, G; Landim, C.. - In: THEORY OF PROBABILITY AND ITS APPLICATIONS. - ISSN 0040-585X. - STAMPA. - 51:1(2006), pp. 2-27. [10.1137/S0040585X97982256]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/143733
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