A Microscopic Derivation of Coupled SPDE's with a KPZ Flavor

Ragaa Ahmed (1) , Cedric Bernardin (2) , Patricia Gonçalves (3) , Marielle Simon (4)

1 Instituto Superior Técnico
2 LJAD - Laboratoire Jean Alexandre Dieudonné
3 Instituto Superior Técnico, Universidade Técnica de Lisboa
4 Paradyse - Systèmes de particules et systèmes dynamiques

We consider an interacting particles system composed of a Hamiltonian part and perturbed by a conservative stochastic noise so that the full system conserves two quantities: energy and volume. The Hamiltonian part is regulated by a scaling parameter vanishing in the limit. We study the form of the fluctuations of these quantities at equilibrium and derive coupled stochastic partial differential equations with a KPZ flavor.

Domaines: Probabilités [math.PR]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Ragaa Ahmed, Cedric Bernardin, Patricia Gonçalves, Marielle Simon. A Microscopic Derivation of Coupled SPDE's with a KPZ Flavor. Annales de l'Institut Henri Poincaré, 2022, 58 (2), ⟨10.1214/21-AIHP1196⟩. ⟨hal-02307963⟩