{
  "id": "2009.00837",
  "version": "v1",
  "published": "2020-09-02T06:27:11.000Z",
  "updated": "2020-09-02T06:27:11.000Z",
  "title": "An entropic proof of cutoff on Ramanujan graphs",
  "authors": [
    "Narutaka Ozawa"
  ],
  "comment": "8 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "It is recently proved by Lubetzky and Peres that the simple random walk on a Ramanujan graph exhibits a cutoff phenomenon, that is to say, the total variation distance of the random walk distribution from the uniform distribution drops abruptly from near $1$ to near $0$. There are already a few alternative proofs of this fact. In this note, we give yet another proof based on functional analysis and entropic consideration.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-02T06:27:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C81",
      "60J10",
      "94A17"
    ],
    "keywords": [
      "ramanujan graph",
      "entropic proof",
      "uniform distribution drops",
      "simple random walk",
      "random walk distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}