CONCURRENT DONSKER-VARADHAN AND HYDRODYNAMICAL LARGE DEVIATIONS
成果类型：
Article
署名作者：
Bertini, Lorenzo; Gabrielli, Davide; Landim, Claudio
署名单位：
Sapienza University Rome; University of L'Aquila
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/22-AOP1619
发表日期：
2023
页码：
1298-1341
关键词：
摘要：
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.
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