Smoothness of the diffusion coefficients for particle systems in continuous space

Arianna Giunti , Chenlin Gu , Jean-Christophe Mourrat (1) , Maximilian Nitzschner

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

For a class of particle systems in continuous space with local interactions, we show that the asymptotic diffusion matrix is an infinitely differentiable function of the density of particles. Our method allows us to identify relatively explicit descriptions of the derivatives of the diffusion matrix in terms of the corrector.

Mots clés: interacting particle system; hydrodynamic limit; bulk diffusion matrix

Domaines: Probabilités [math.PR]

Arianna Giunti, Chenlin Gu, Jean-Christophe Mourrat, Maximilian Nitzschner. Smoothness of the diffusion coefficients for particle systems in continuous space. Communications in Contemporary Mathematics, 2023, 25 (03), ⟨10.1142/S0219199722500274⟩. ⟨hal-03480515⟩