{
  "id": "1112.1003",
  "version": "v2",
  "published": "2011-12-05T17:11:09.000Z",
  "updated": "2015-03-01T13:43:31.000Z",
  "title": "The Parisi ultrametricity conjecture",
  "authors": [
    "Dmitry Panchenko"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1108.0379",
  "journal": "Ann. of Math. (2), Vol. 177, No. 1 (2013) 383-393",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we prove that the support of a random measure on the unit ball of a separable Hilbert space that satisfies the Ghirlanda-Guerra identities must be ultrametric with probability one. This implies the Parisi ultrametricity conjecture in mean-field spin glass models, such as the Sherrington-Kirkpatrick and mixed $p$-spin models, for which Gibbs' measures are known to satisfy the Ghirlanda-Guerra identities in the thermodynamic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-12-05T17:11:09.000Z",
      "comment": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-03-01T13:43:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "parisi ultrametricity conjecture",
      "ghirlanda-guerra identities",
      "mean-field spin glass models",
      "unit ball",
      "separable hilbert space"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1112.1003P"
    }
  }
}