{
  "id": "0706.3500",
  "version": "v3",
  "published": "2007-06-24T06:57:31.000Z",
  "updated": "2009-08-02T10:16:06.000Z",
  "title": "Spin glasses and Stein's method",
  "authors": [
    "Sourav Chatterjee"
  ],
  "comment": "29 pages. Final version. To appear in PTRF",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We introduce some applications of Stein's method in the high temperature analysis of spin glasses. Stein's method allows the direct analysis of the Gibbs measure without having to create a cavity. Another advantage is that it gives limit theorems with total variation error bounds, although the bounds can be suboptimal. A surprising byproduct of our analysis is a relatively transparent explanation of the Thouless-Anderson-Palmer system of equations. Along the way, we develop Stein's method for mixtures of two Gaussian densities.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-08-02T10:16:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "steins method",
      "spin glasses",
      "total variation error bounds",
      "high temperature analysis",
      "gaussian densities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0706.3500C"
    }
  }
}