{
  "id": "1906.11544",
  "version": "v1",
  "published": "2019-06-27T10:42:22.000Z",
  "updated": "2019-06-27T10:42:22.000Z",
  "title": "Total variation cutoff for the flip-transpose top with random shuffle",
  "authors": [
    "Subhajit Ghosh"
  ],
  "comment": "25 pages, 2 figures, 1 table",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a random walk on the hyperoctahedral group $B_n$ generated by the signed permutations of the forms $(i,n)$ and $(-i,n)$ for $1\\leq i\\leq n$. We call this the flip-transpose top with random shuffle on $B_n$. We find the spectrum of the transition probability matrix for this shuffle. We prove that the mixing time for this shuffle is of order $n\\log n$. We also show that this shuffle exhibits the cutoff phenomenon. In the appendix, we show that a similar random walk on the demihyperoctahedral group $D_n$ also has a cutoff at $\\left(n-\\frac{1}{2}\\right)\\log n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-27T10:42:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60B15",
      "60C05"
    ],
    "keywords": [
      "total variation cutoff",
      "random shuffle",
      "flip-transpose",
      "similar random walk",
      "transition probability matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}