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.
|Journal||Annales de l'Institut Henri Poincaré - Probabilités et Statistiques|
|Number of pages||40|
|Publication status||Published - 2022|
- Equilibrium fluctuations
- Ornstein-Uhlenbeck process
- Interacting particle systems with long jumps
- Boundary conditions