{
  "id": "1902.00978",
  "version": "v1",
  "published": "2019-02-03T22:19:45.000Z",
  "updated": "2019-02-03T22:19:45.000Z",
  "title": "Central limit theorem for peaks of a random permutation in a fixed conjugacy class of $S_n$",
  "authors": [
    "Jason Fulman",
    "Gene B. Kim",
    "Sangchul Lee"
  ],
  "comment": "21 pages, 1 figure",
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "The number of peaks of a random permutation is known to be asymptotically normal. We give a new proof of this and prove a central limit theorem for the distribution of peaks in a fixed conjugacy class of the symmetric group. Our technique is to apply ``analytic combinatorics'' to study a complicated but exact generating function for peaks in a given conjugacy class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-03T22:19:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central limit theorem",
      "fixed conjugacy class",
      "random permutation",
      "symmetric group",
      "analytic combinatorics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}