{
  "id": "1410.5032",
  "version": "v1",
  "published": "2014-10-19T03:28:15.000Z",
  "updated": "2014-10-19T03:28:15.000Z",
  "title": "Monotonicity of Avoidance Coupling on $K_N$",
  "authors": [
    "Ohad Noy Feldheim"
  ],
  "comment": "8 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "Answering a question by Angel, Holroyd, Martin, Wilson and Winkler, we show that the maximal number of non-colliding coupled simple random walks on the complete graph $K_N$, which take turns, moving one at a time, is monotone in $N$. We use this fact to couple $\\lceil \\frac N4 \\rceil$ such walks on $K_N$, improving the previous $\\Omega(N/\\log N)$ lower bound of Angel et al. To do this we introduce a new generalization of simple avoidance coupling which we call partially-ordered simple avoidance coupling.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-19T03:28:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10"
    ],
    "keywords": [
      "monotonicity",
      "simple avoidance coupling",
      "non-colliding coupled simple random walks",
      "maximal number",
      "complete graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.5032N"
    }
  }
}