Density Fluctuations for the Multi-Species Stirring Process

Francesco Casini (), Cristian Giardinà and Frank Redig
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Francesco Casini: Università di Modena e Reggio Emilia
Cristian Giardinà: Università di Modena e Reggio Emilia
Frank Redig: TU Delft

Journal of Theoretical Probability, 2024, vol. 37, issue 4, 3317-3354

Abstract: 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.

Keywords: Equilibrium density fluctuations; Multi-species; Ornstein–Uhlenbeck; Reaction–diffusion; 60K35; 82C22 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01340-6

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