{
  "id": "2204.03470",
  "version": "v1",
  "published": "2022-04-07T14:33:21.000Z",
  "updated": "2022-04-07T14:33:21.000Z",
  "title": "Limits of Pólya urns with innovations",
  "authors": [
    "Jean Bertoin"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a version of the classical P\\'olya urn scheme which incorporates innovations. The space $S$ of colors is an arbitrary measurable set. After each sampling of a ball in the urn, one returns $C$ balls of the same color and additional balls of different colors given by some finite point process $\\xi$ on $S$. When the number of steps goes to infinity, the empirical distribution of the colors in the urn converges to the normalized intensity measure of $\\xi$, and we analyze the fluctuations. The ratio $\\rho= E(C)/E(R)$ of the average number of copies to the average total number of balls returned plays a key role.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-04-07T14:33:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60G44",
      "60J85",
      "62G30"
    ],
    "keywords": [
      "pólya urns",
      "finite point process",
      "classical polya urn scheme",
      "average total number",
      "additional balls"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}