{
  "id": "1803.04207",
  "version": "v1",
  "published": "2018-03-12T11:46:17.000Z",
  "updated": "2018-03-12T11:46:17.000Z",
  "title": "A.s. convergence for infinite colour Pólya urns associated with random walks",
  "authors": [
    "Svante Janson"
  ],
  "comment": "30 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider P\\'olya urns with infinitely many colours that are of a random walk type, in two related version. We show that the colour distribution a.s., after rescaling, converges to a normal distribution, assuming only second moments on the offset distribution. This improves results by Bandyopadhyay and Thacker (2014--2017; convergence in probability), and Mailler and Marckert (2017; a.s. convergence assuming exponential moment).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-12T11:46:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05"
    ],
    "keywords": [
      "infinite colour pólya urns",
      "random walk type",
      "convergence assuming exponential moment",
      "polya urns",
      "offset distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}