{
  "id": "1811.02039",
  "version": "v1",
  "published": "2018-11-05T21:26:24.000Z",
  "updated": "2018-11-05T21:26:24.000Z",
  "title": "Random walks generated by Ewens distribution on the symmetric group",
  "authors": [
    "Alperen Y. Özdemir"
  ],
  "comment": "24 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies Markov chains on the symmetric group $S_n$ where the transition probabilities are given by Ewens distribution with parameter $\\theta>0$. The eigenvalues are identified to be content polynomials of partitions divided by n$th$ rising factorial of $\\theta.$ The mixing time analysis is carried out for two cases: If $\\theta$ is a constant integer, the chain is fast enough that the mixing time does not depend on $n.$ If $\\theta=n$, the chain exhibits a total variation cutoff at $\\frac{\\log n}{\\log 2}$ steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-05T21:26:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05",
      "05E10"
    ],
    "keywords": [
      "ewens distribution",
      "symmetric group",
      "random walks",
      "paper studies markov chains",
      "total variation cutoff"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}