{
  "id": "1306.5008",
  "version": "v2",
  "published": "2013-06-20T21:59:58.000Z",
  "updated": "2014-11-12T21:33:56.000Z",
  "title": "Likelihood Orders for some Random Walks on the Symmetric Group",
  "authors": [
    "Megan Bernstein"
  ],
  "categories": [
    "math.CO",
    "math.PR"
  ],
  "abstract": "Several cycle lexicographical orders are found to describe the relative likelihood of elements of the random walks on the symmetric group generated by the conjugacy classes of transpositions, 3-cycles, and n-cycles. Spectral analysis finds sufficient time for the orders to hold. This partially answers a conjecture that the n-cycles are the least likely elements of the transposition walk on the symmetric group. A likelihood order contributes to understanding the total variation distance and separation distance for a random walk.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-06-20T21:59:58.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-11-12T21:33:56.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "random walk",
      "symmetric group",
      "spectral analysis finds sufficient time",
      "total variation distance",
      "likelihood order contributes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1306.5008B"
    }
  }
}