{
  "id": "1908.06240",
  "version": "v1",
  "published": "2019-08-17T04:43:59.000Z",
  "updated": "2019-08-17T04:43:59.000Z",
  "title": "Markov chains with exponential return times are finitary",
  "authors": [
    "Omer Angel",
    "Yinon Spinka"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an i.i.d. process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of $\\mathbb{Z}$ is a finitary factor of an i.i.d. process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-17T04:43:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60G10"
    ],
    "keywords": [
      "exponential return times",
      "finitary factor",
      "exponential tails",
      "ergodic markov chain",
      "stationary renewal process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}