Large deviations of the empirical current in interacting particle systems
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.
Cite
@article{arxiv.math/0512394,
title = {Large deviations of the empirical current in interacting particle systems},
author = {L. Bertini and A. De Sole and D. Gabrielli and G. Jona-Lasinio and C. Landim},
journal= {arXiv preprint arXiv:math/0512394},
year = {2015}
}
Comments
26 pages