Nonconvex interactions in mean-field spin glasses
Probability
2021-06-02 v8 Disordered Systems and Neural Networks
Abstract
We propose a conjecture for the limit 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 of 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.
Cite
@article{arxiv.2004.01679,
title = {Nonconvex interactions in mean-field spin glasses},
author = {Jean-Christophe Mourrat},
journal= {arXiv preprint arXiv:2004.01679},
year = {2021}
}
Comments
51 pages, final version, to appear in Probab. Math. Phys