{
  "id": "1910.14482",
  "version": "v1",
  "published": "2019-10-31T14:19:47.000Z",
  "updated": "2019-10-31T14:19:47.000Z",
  "title": "Extending the Parisi formula along a Hamilton-Jacobi equation",
  "authors": [
    "J. -C. Mourrat",
    "D. Panchenko"
  ],
  "comment": "16 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the free energy of mixed $p$-spin spin glass models enriched with an additional magnetic field given by the canonical Gaussian field associated with a Ruelle probability cascade. We prove that this free energy converges to the Hopf-Lax solution of a certain Hamilton-Jacobi equation. Using this result, we give a new representation of the free energy of mixed $p$-spin models with soft spins.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-31T14:19:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "82B44",
      "82D30"
    ],
    "keywords": [
      "hamilton-jacobi equation",
      "parisi formula",
      "spin spin glass models",
      "ruelle probability cascade",
      "additional magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}