{
  "id": "0908.2038",
  "version": "v2",
  "published": "2009-08-14T10:56:40.000Z",
  "updated": "2014-02-28T13:51:03.000Z",
  "title": "Optimal co-adapted coupling for a random walk on the hyper-complete-graph",
  "authors": [
    "Stephen B. Connor"
  ],
  "comment": "20 pages, 1 figure",
  "journal": "J. Appl. Probab. Volume 50, Number 4 (2013), 1117-1130",
  "doi": "10.1239/jap/1389370103",
  "categories": [
    "math.PR"
  ],
  "abstract": "The problem of constructing an optimal co-adapted coupling for a pair of symmetric random walks on $Z_2^d$ was considered by Connor and Jacka (2008), and the existence of a coupling which is stochastically fastest in the class of all such co-adapted couplings was demonstrated. In this paper we show how to generalise this construction to an optimal co-adapted coupling for the continuous-time symmetric random walk on $K_n^d$, where $K_n$ is the complete graph with $n$ vertices. Moreover, we show that although this coupling is not maximal for any $n$ (i.e. it does not achieve equality in the coupling inequality), it does tend to a maximal coupling as $n\\to\\infty$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-02-28T13:51:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "93E20",
      "60J27"
    ],
    "keywords": [
      "optimal co-adapted coupling",
      "continuous-time symmetric random walk",
      "hyper-complete-graph",
      "achieve equality",
      "complete graph"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0908.2038C"
    }
  }
}