{
  "id": "0810.0743",
  "version": "v4",
  "published": "2008-10-04T02:08:23.000Z",
  "updated": "2010-01-27T09:30:18.000Z",
  "title": "A connection between the Ghirlanda--Guerra identities and ultrametricity",
  "authors": [
    "Dmitry Panchenko"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AOP484 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2010, Vol. 38, No. 1, 327-347",
  "doi": "10.1214/09-AOP484",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a symmetric positive definite weakly exchangeable infinite random matrix and show that, under the technical condition that its elements take a finite number of values, the Ghirlanda--Guerra identities imply ultrametricity.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-01-27T09:30:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82B44"
    ],
    "keywords": [
      "ghirlanda-guerra identities",
      "ultrametricity",
      "positive definite weakly exchangeable",
      "connection",
      "weakly exchangeable infinite random matrix"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.0743P"
    }
  }
}