{
  "id": "1208.4716",
  "version": "v1",
  "published": "2012-08-23T10:49:34.000Z",
  "updated": "2012-08-23T10:49:34.000Z",
  "title": "The Role of Kemeny's Constant in Properties of Markov Chains",
  "authors": [
    "Jeffrey J. Hunter"
  ],
  "comment": "13 pages",
  "journal": "Communications in Statistics - Theory and Methods, 43:7, 1309-1321, 2014",
  "doi": "10.1080/03610926.2012.741742",
  "categories": [
    "math.PR"
  ],
  "abstract": "In a finite state irreducible Markov chain with stationary probabilities \\pi_i and mean first passage times m_(ij) (mean recurrence time when i = j) it was first shown by Kemeny and Snell (1960) that \\sum_j \\pi_j m_(ij) is a constant K, not depending on i. This constant has since become known as Kemeny's constant. A variety of techniques for finding expressions and various bounds for K are derived. The main interpretation focuses on its role as the expected time to mixing in a Markov chain. Various applications are considered including perturbation results, mixing on directed graphs and its relation to the Kirchhoff index of regular graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-08-23T10:49:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10"
    ],
    "keywords": [
      "kemenys constant",
      "finite state irreducible markov chain",
      "properties",
      "mean first passage times",
      "main interpretation focuses"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1208.4716H"
    }
  }
}