{
  "id": "1906.08471",
  "version": "v1",
  "published": "2019-06-20T07:26:11.000Z",
  "updated": "2019-06-20T07:26:11.000Z",
  "title": "Parisi's formula is a Hamilton-Jacobi equation in Wasserstein space",
  "authors": [
    "Jean-Christophe Mourrat"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "cond-mat.dis-nn"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T07:26:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "hamilton-jacobi equation",
      "wasserstein space",
      "parisis formula",
      "mean-field spin glass models",
      "probability measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}