{
  "id": "1601.02898",
  "version": "v1",
  "published": "2016-01-12T15:10:20.000Z",
  "updated": "2016-01-12T15:10:20.000Z",
  "title": "The Tracy-Widom distribution is not infinitely divisible",
  "authors": [
    "J. Armando Domínguez-Molina"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The classical infinite divisibility of distributions related to eigenvalues of some random matrix ensembles is investigated. It is proved that the $\\beta$-Tracy-Widom distribution, which is the limiting distribution of the largest eigenvalue of a $\\beta$-Hermite ensemble, is not infinitely divisible. Furthermore, for each fixed $N \\ge 2$ it is proved that the largest eigenvalue of a GOE/GUE random matrix is not infinitely divisible.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-12T15:10:20.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "tracy-widom distribution",
      "infinitely divisible",
      "largest eigenvalue",
      "goe/gue random matrix",
      "random matrix ensembles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160102898D"
    }
  }
}