{
  "id": "2006.04840",
  "version": "v1",
  "published": "2020-06-08T18:04:16.000Z",
  "updated": "2020-06-08T18:04:16.000Z",
  "title": "Random derangements and the Ewens Sampling Formula",
  "authors": [
    "Poly H. da Silva",
    "Arash Jamshidpey",
    "Simon Tavaré"
  ],
  "comment": "16 pages, 9 tables",
  "categories": [
    "math.PR",
    "stat.ME"
  ],
  "abstract": "We study derangements of $\\{1,2,\\ldots,n\\}$ under the Ewens distribution with parameter $\\theta$. We give the moments and marginal distributions of the cycle counts, the number of cycles, and asymptotic distributions for large $n$. We develop a $\\{0,1\\}$-valued non-homogeneous Markov chain with the property that the counts of lengths of spacings between the 1s have the derangement distribution. This chain, an analog of the so-called Feller Coupling, provides a simple way to simulate derangements in time independent of $\\theta$ for a given $n$ and linear in the size of the derangement.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-08T18:04:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "60J10",
      "65C05",
      "65C40"
    ],
    "keywords": [
      "ewens sampling formula",
      "random derangements",
      "marginal distributions",
      "study derangements",
      "asymptotic distributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}