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Article Dans Une Revue The Annals of Applied Probability Année : 2023

Concurrent Donsker-Varadhan and hydrodynamical large deviations

Résumé

We consider the weakly asymmetric exclusion process on the $d$-dimensional torus. We prove a large deviations principle for the time averaged 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 considering the large time behavior of the hydrodynamical rate function. The large deviations asymptotic of the time averaged current is then deduced by contraction principle. The structure of the minimizers of this variational problem corresponds to the possible occurrence of dynamical phase transitions.

Dates et versions

hal-03897401 , version 1 (13-12-2022)

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Lorenzo Bertini, Davide Gabrielli, Claudio Landim. Concurrent Donsker-Varadhan and hydrodynamical large deviations. The Annals of Applied Probability, 2023, 51 (4), ⟨10.1214/22-AOP1619⟩. ⟨hal-03897401⟩
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