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Large deviations of the empirical current in interacting particle systems

L. Bertini·A. De Sole·D. Gabrielli·G. Jona-Lasinio·C. Landim
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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.

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L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, C. Landim. 2005-12-16. Large deviations of the empirical current in interacting particle systems. https://doi.org/10.1137/s0040585x97982256

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