Nonconvex interactions in mean-field spin glasses
Résumé
We propose a conjecture for the limit free energy of mean-field spin glasses with a bipartite structure, and show that the conjectured limit is an upper bound. The conjectured limit is described in terms of the solution to an infinite-dimensional Hamilton-Jacobi equation. A fundamental difficulty of the problem is that the nonlinearity in this equation is not convex. We also question the possibility to characterize this conjectured limit in terms of a saddle-point problem.
Domaines
Probabilités [math.PR]
Origine : Fichiers produits par l'(les) auteur(s)