{
  "id": "1910.02856",
  "version": "v1",
  "published": "2019-10-07T15:36:39.000Z",
  "updated": "2019-10-07T15:36:39.000Z",
  "title": "Combinatorial considerations on the invariant measure of a stochastic matrix",
  "authors": [
    "Artur Stephan"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "The invariant measure is a fundamental object in the theory of Markov processes. In finite dimensions a Markov process is defined by transition rates of the corresponding stochastic matrix. The Markov tree theorem provides an explicit representation of the invariant measure of a stochastic matrix. In this note, we given a simple and purely combinatorial proof of the Markov tree theorem. In the symmetric case of detailed balance, the statement and the proof simplifies even more.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-07T15:36:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60Jxx"
    ],
    "keywords": [
      "invariant measure",
      "stochastic matrix",
      "combinatorial considerations",
      "markov tree theorem",
      "markov process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}