We consider the weakly asymmetric exclusion process on the d- dimensional torus. We prove a large deviations principle for the time av- eraged empirical density and current in the joint limit in which both the time interval and the number of particles diverge. This result is obtained both by analyzing the variational convergence, as the number of particles diverges, of the Donsker-Varadhan functional for the empirical process and by consider- ing the large time behavior of the hydrodynamical rate function. The large deviations asymptotic of the time averaged current is then deduced by con- traction principle. The structure of the minimizers of this variational problem corresponds to the possible occurrence of dynamical phase transitions.
Concurrent Donsker-Varadhan and hydrodynamical large deviations / Bertini, L.; Gabrielli, D.; Landim, C.. - In: ANNALS OF PROBABILITY. - ISSN 0091-1798. - 51:(2023), pp. 1298-1341. [10.1214/22-AOP1619]
Concurrent Donsker-Varadhan and hydrodynamical large deviations
Bertini, L.;
2023
Abstract
We consider the weakly asymmetric exclusion process on the d- dimensional torus. We prove a large deviations principle for the time av- eraged empirical density and current in the joint limit in which both the time interval and the number of particles diverge. This result is obtained both by analyzing the variational convergence, as the number of particles diverges, of the Donsker-Varadhan functional for the empirical process and by consider- ing the large time behavior of the hydrodynamical rate function. The large deviations asymptotic of the time averaged current is then deduced by con- traction principle. The structure of the minimizers of this variational problem corresponds to the possible occurrence of dynamical phase transitions.File | Dimensione | Formato | |
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