Equilibrium fluctuations for diffusive symmetric exclusion with long jumps and infinitely extended reservoirs

C. Bernardin, P. Goncalves, M. Jara, S. Scotta

Research output: Contribution to journalA1: Web of Science-article

Abstract

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.

Original languageEnglish
JournalAnnales de l'Institut Henri Poincaré - Probabilités et Statistiques
Volume58
Issue number1
Pages (from-to)303-342
Number of pages40
ISSN0246-0203
DOIs
Publication statusPublished - 2022
Externally publishedYes

Keywords

  • Equilibrium fluctuations
  • Ornstein-Uhlenbeck process
  • Interacting particle systems with long jumps
  • Boundary conditions
  • SLOW

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