EQUILIBRIUM FLUCTUATIONS FOR DIFFUSIVE SYMMETRIC EXCLUSION WITH LONG JUMPS AND INFINITELY EXTENDED RESERVOIRS

Creators: Bernardin, Cedric; Goncalves, Patricia; Jara, Milton; Scotta, Stefano

Others:: Laboratoire Jean Alexandre Dieudonné (JAD) ; Université Nice Sophia Antipolis (1965 - 2019) (UNS) ; COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA); ANR-15-CE40-0020,LSD,Modèles stochastiques en grande dimension pour la physique statistique hors équilibre(2015); European Project: 715734,H2020,HyLEF(2016)

Description

We provide a complete description of the equilibrium fluctuations for diffusive symmetric exclusion processes with long jumps in contact with infinitely extended reservoirs and prove that they behave as generalized Ornstein-Uhlenbeck processes with various boundary conditions, depending mainly on the strength of the reservoirs. On the way, we also give a general statement about uniqueness of the Ornstein-Uhlenbeck process originated by the microscopic dynamics of the underlying interacting particle systems and adapt it to our study.

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EQUILIBRIUM FLUCTUATIONS FOR DIFFUSIVE SYMMETRIC EXCLUSION WITH LONG JUMPS AND INFINITELY EXTENDED RESERVOIRS

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