Large Deviations of the Empirical Current in Interacting Particle Systems

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 ave...

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Bibliographic Details
Published inTheory of probability and its applications Vol. 51; no. 1; pp. 2 - 27
Main Authors Bertini, L., De Sole, A., Gabrielli, D., Jona‐Lasinio, G., Landim, C.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 2007
Subjects
Inequality
Markov analysis
Phase transitions
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Summary: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.
ISSN:0040-585X
1095-7219
DOI:10.1137/S0040585X97982256