{
  "id": "0709.1514",
  "version": "v2",
  "published": "2007-09-11T01:03:17.000Z",
  "updated": "2008-05-04T17:28:48.000Z",
  "title": "On differentiability of the Parisi formula",
  "authors": [
    "Dmitry Panchenko"
  ],
  "journal": "Vol. 13 (2008) Elect. Comm. in Probab. 241-247",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "It was proved by Michel Talagrand in [10] that the Parisi formula for the free energy in the Sherrington-Kirkpatrick model is differentiable with respect to inverse temperature parameter. We present a simpler proof of this result by using approximate solutions in the Parisi formula and give one example of application of the differentiability to prove non self-averaging of the overlap outside of the replica symmetric region.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2008-05-04T17:28:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "parisi formula",
      "differentiability",
      "inverse temperature parameter",
      "replica symmetric region",
      "michel talagrand"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0709.1514P"
    }
  }
}