{
  "id": "2004.01679",
  "version": "v1",
  "published": "2020-04-03T17:21:25.000Z",
  "updated": "2020-04-03T17:21:25.000Z",
  "title": "Nonconvex interactions in mean-field spin glasses",
  "authors": [
    "Jean-Christophe Mourrat"
  ],
  "comment": "44 pages",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-03T17:21:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "mean-field spin glasses",
      "nonconvex interactions",
      "conjectured limit",
      "infinite-dimensional hamilton-jacobi equation",
      "bipartite structure"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}