{
  "id": "1511.02810",
  "version": "v1",
  "published": "2015-11-09T19:23:30.000Z",
  "updated": "2015-11-09T19:23:30.000Z",
  "title": "Exponentials and $R$-recurrent random walks on groups",
  "authors": [
    "M. G. Shur"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "On a locally compact group $E$ with countable base, we consider a random walk $X$ that has a unique (up to a positive factor) $r$-invariant measure for some $r>0$. Under some weak conditions on the measure, there is a unique continuous exponential on $E$ naturally associated with $X$. It follows that there exists an $R$-recurrent random walk in the sense of Tweedie on $E$ if and only if $E$ is a recurrent group and there exists a Harris random walk on~$E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-09T19:23:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "recurrent random walk",
      "harris random walk",
      "invariant measure",
      "weak conditions",
      "unique continuous exponential"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151102810S"
    }
  }
}