Large deviations of the empirical current in interacting particle systems

Details Large deviations of the empirical current in interacting particle systems Large deviations of the empirical current in interacting particle systems

2005-12-16

arxiv.org/abs/math/0512394v1

Theory Probab. Appl. (2007) 51, 2-27

Mathematics

Probability

26 pages

Scientific paper

10.1137/S0040585X97982256

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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