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.
2023
Exclusion processes; hydrodynamical limits; large deviations; empirical process; dynamical phase transitions
01 Pubblicazione su rivista::01a Articolo in rivista
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]
File allegati a questo prodotto
File Dimensione Formato  
Bertini_postprint_Concurrent_2023.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 460.98 kB
Formato Adobe PDF
460.98 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1680749
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? 0
social impact