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

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