{
  "id": "1302.3738",
  "version": "v1",
  "published": "2013-02-15T12:43:00.000Z",
  "updated": "2013-02-15T12:43:00.000Z",
  "title": "On the free Gamma distributions",
  "authors": [
    "Uffe Haagerup",
    "Steen Thorbjornsen"
  ],
  "comment": "31 pages, 4 figures",
  "categories": [
    "math.PR",
    "math.OA"
  ],
  "abstract": "For each positive number $\\alpha$ we study the analog $\\nu_alpha$ in free probability of the classical Gamma distribution with parameter $\\alpha$. We prove that $\\nu_\\alpha$ is absolutely continuous and establish the main properties of the density, including analyticity and unimodality. We study further the asymptotic behavior of $\\nu_\\alpha$ as $\\alpha\\downarrow0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-02-15T12:43:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46L54",
      "60E07"
    ],
    "keywords": [
      "free gamma distributions",
      "free probability",
      "classical gamma distribution",
      "main properties",
      "asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}