{
  "id": "1411.1463",
  "version": "v1",
  "published": "2014-11-06T01:09:42.000Z",
  "updated": "2014-11-06T01:09:42.000Z",
  "title": "One-dependent coloring by finitary factors",
  "authors": [
    "Alexander E. Holroyd"
  ],
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Holroyd and Liggett recently proved the existence of a stationary 1-dependent 4-coloring of the integers, the first stationary k-dependent q-coloring for any k and q. That proof specifies a consistent family of finite-dimensional distributions, but does not yield a probabilistic construction on the whole integer line. Here we prove that the process can be expressed as a finitary factor of an i.i.d. process. The factor is described explicitly, and its coding radius obeys power-law tail bounds.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-06T01:09:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G10",
      "05C15",
      "60C05"
    ],
    "keywords": [
      "finitary factor",
      "one-dependent coloring",
      "radius obeys power-law tail bounds",
      "coding radius obeys power-law tail",
      "first stationary k-dependent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.1463H"
    }
  }
}