Archive ouverte HAL – Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation

Thibault Bonnemain 1, 2 Denis Ullmo 1

Thibault Bonnemain, Denis Ullmo. Mean field games in the weak noise limit : A WKB approach to the Fokker–Planck equation. Physica A: Statistical Mechanics and its Applications, Elsevier, 2019, 523, pp.310-325. ⟨10.1016/j.physa.2019.01.143⟩. ⟨hal-02102129⟩

Motivated by the study of a Mean Field Game toy model called the "seminar problem", we consider the Fokker-Planck equation in the small noise regime for a specific drift field. This gives us the opportunity to discuss the application to diffusion problem of the WKB approach "a la Maslov", making it possible to solve directly the time dependant problem in an especially transparent way.

  • 1. LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
  • 2. LPTM - Laboratoire de Physique Théorique et Modélisation