{
  "id": "1502.04160",
  "version": "v1",
  "published": "2015-02-14T02:38:57.000Z",
  "updated": "2015-02-14T02:38:57.000Z",
  "title": "An Exercise (?) in Fourier Analysis on the Heisenberg Group",
  "authors": [
    "Daniel Bump",
    "Persi Diaconis",
    "Angela Hicks",
    "Laurent Miclo",
    "Harold Widom"
  ],
  "comment": "24 pages, 6 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "Let H(n) be the group of 3x3 uni-uppertriangular matrices with entries in Z/nZ, the integers mod n. We show that the simple random walk converges to the uniform distribution in order n^2 steps. The argument uses Fourier analysis and is surprisingly challenging. It introduces novel techniques for bounding the spectrum which are useful for a variety of walks on a variety of groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-14T02:38:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60B15"
    ],
    "keywords": [
      "fourier analysis",
      "heisenberg group",
      "simple random walk converges",
      "3x3 uni-uppertriangular matrices",
      "novel techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}