Hamilton-Jacobi equations for mean-field disordered systems

Jean-Christophe Mourrat (1)

1 DMA - Département de Mathématiques et Applications - ENS Paris

We argue that Hamilton-Jacobi equations provide a convenient and intuitive approach for studying the large-scale behavior of mean-field disordered systems. This point of view is illustrated on the problem of inference of a rank-one matrix. We compute the large-scale limit of the free energy by showing that it satisfies an approximate Hamilton-Jacobi equation with asymptotically vanishing viscosity parameter and error term.

Mots clés: spin glass; statistical inference; Hamilton-Jacobi equation

Domaines: Probabilités [math.PR]

Jean-Christophe Mourrat. Hamilton-Jacobi equations for mean-field disordered systems. Annales Henri Lebesgue, 2021, ⟨10.5802/ahl.77⟩. ⟨hal-01913504⟩