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Density Fluctuations for the Multi-Species Stirring Process

Author

Listed:
  • Francesco Casini

    (Università di Modena e Reggio Emilia
    Università di Parma)

  • Cristian Giardinà

    (Università di Modena e Reggio Emilia)

  • Frank Redig

    (TU Delft)

Abstract

We study the density fluctuations at equilibrium of the multi-species stirring process, a natural multi-type generalization of the symmetric (partial) exclusion process. In the diffusive scaling limit, the resulting process is a system of infinite-dimensional Ornstein–Uhlenbeck processes that are coupled in the noise terms. This shows that at the level of equilibrium fluctuations the species start to interact, even though at the level of the hydrodynamic limit each species diffuses separately. We consider also a generalization to a multi-species stirring process with a linear reaction term arising from species mutation. The general techniques used in the proof are based on the Dynkin martingale approach, combined with duality for the computation of the covariances.

Suggested Citation

  • Francesco Casini & Cristian Giardinà & Frank Redig, 2024. "Density Fluctuations for the Multi-Species Stirring Process," Journal of Theoretical Probability, Springer, vol. 37(4), pages 3317-3354, November.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:4:d:10.1007_s10959-024-01340-6
    DOI: 10.1007/s10959-024-01340-6
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    References listed on IDEAS

    as
    1. Floreani, Simone & Redig, Frank & Sau, Federico, 2021. "Hydrodynamics for the partial exclusion process in random environment," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 124-158.
    2. Gonçalves, Patricia & Misturini, Ricardo & Occelli, Alessandra, 2023. "Hydrodynamics for the ABC model with slow/fast boundary," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 350-384.
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