{
  "id": "1712.00210",
  "version": "v1",
  "published": "2017-12-01T06:59:11.000Z",
  "updated": "2017-12-01T06:59:11.000Z",
  "title": "An upper bound on the size of avoidance couplings on $K_n$",
  "authors": [
    "Erik Bates",
    "Lisa Sauermann"
  ],
  "comment": "7 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show that a coupling of non-colliding simple random walkers on the complete graph on $n$ vertices can include at most $n - \\log n$ walkers. This improves the only previously known upper bound of $n-2$ due to Angel, Holroyd, Martin, Wilson, and Winkler (Electron. Commun. Probab. 18, 2013).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-01T06:59:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "05C81"
    ],
    "keywords": [
      "upper bound",
      "avoidance couplings",
      "non-colliding simple random walkers",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}