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.
Keywords
spin glass, Hamilton–Jacobi equation, Wasserstein space
