Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space

Jean-Christophe Mourrat (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Parisi's formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We show that this quantity can be recast as the solution of a Hamilton-Jacobi equation in the Wasserstein space of probability measures on the positive half-line.

Domaines: Probabilités [math.PR]

Jean-Christophe Mourrat. Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space. Canadian Journal of Mathematics = Journal Canadien de Mathématiques, 2022, ⟨10.4153/S0008414X21000031⟩. ⟨hal-03581471⟩