{
  "id": "1503.09165",
  "version": "v1",
  "published": "2015-03-31T19:08:12.000Z",
  "updated": "2015-03-31T19:08:12.000Z",
  "title": "Optimal stopping time and halting set for total variation distance",
  "authors": [
    "Agnes Coquio"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "An aperiodic and irreducible Markov chain on a finite state space converges to its stationary distribution. When convergence to equilibrium is measured by total variation distance, there exists an optimal coupling and a maximal coupling time. In this article, the maximal coupling time is compared to the hitting time of a specific state or set. Such sets, named halting sets, are studied in the case of symmetric birth-and-death chains and in some other examples. Some applications to the cutoff phenomenon are given. These results yield new methods to calculate cutoff times for some monotone birth-and death chains without the lazy hypothesis .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-31T19:08:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "total variation distance",
      "optimal stopping time",
      "halting set",
      "maximal coupling time",
      "finite state space converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}