{
  "id": "1807.08539",
  "version": "v1",
  "published": "2018-07-23T11:32:08.000Z",
  "updated": "2018-07-23T11:32:08.000Z",
  "title": "Total variation cutoff for the transpose top-$2$ with random shuffle",
  "authors": [
    "Subhajit Ghosh"
  ],
  "comment": "20 pages, 1 table, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, we investigate the properties of a random walk on the alternating group $A_n$ generated by $3$-cycles of the form $(i,n-1,n)$ and $(i,n,n-1)$. We call this the transpose top-$2$ with random shuffle. We find the spectrum of the transition matrix of this shuffle. We show that the mixing time is of order $\\left(n-\\frac{3}{2}\\right)\\log n$ and prove that there is a total variation cutoff for this shuffle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-23T11:32:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "total variation cutoff",
      "random shuffle",
      "transition matrix",
      "random walk",
      "properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}