{
  "id": "1106.3984",
  "version": "v1",
  "published": "2011-06-20T18:37:20.000Z",
  "updated": "2011-06-20T18:37:20.000Z",
  "title": "Ghirlanda-Guerra identities and ultrametricity: An elementary proof in the discrete case",
  "authors": [
    "Dmitry Panchenko"
  ],
  "journal": "C. R. Acad. Sci. Paris, Ser. I {349} (2011) 813-816",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In this paper we give another proof of the fact that a random overlap array, which satisfies the Ghirlanda-Guerra identities and whose elements take values in a finite set, is ultrametric with probability one. The new proof bypasses random change of density invariance principles for directing measures of such arrays and, in addition to the Dobvysh-Sudakov representation, is based only on elementary algebraic consequences of the Ghirlanda-Guerra identities.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-20T18:37:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "ghirlanda-guerra identities",
      "discrete case",
      "elementary proof",
      "ultrametricity",
      "proof bypasses random change"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.3984P"
    }
  }
}