The Parisi formula and beyond: a PDE approach to disordered systems
Mercredi, 12 Février, 2025 - 17:00
Résumé :
Disordered systems appear in many branches of physics from condensed matter to neural networks. In this talk we introduce disordered systems trough the dean’s problem and the example of the Sherrington-Kirkpatrick model. As initially conjectured by physicists, the free energy of this model can be expressed via a variationnal formula. We will explain how this formula is related to an infinite dimensional Hamilton-Jacobi equation and how this observation allows to formulate conjectures for the value of the free energy of more complicated models. If time allows, we will explain how this philosophy can be used to describe the free energy of a simple disorderless model, the Currie-Weiss model.
Institution de l'orateur :
ENS Lyon
Thème de recherche :
Compréhensible
Salle :
4