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

Abstract

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.

19 pages

References in corpus (3)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Hamilton-Jacobi equations for finite-rank matrix inference
• Guerra's interpolation using Derrida-Ruelle cascades