{
  "id": "2310.00159",
  "version": "v1",
  "published": "2023-09-29T21:49:39.000Z",
  "updated": "2023-09-29T21:49:39.000Z",
  "title": "Pólya urns on hypergraphs",
  "authors": [
    "Pedro Alves",
    "Matheus Barros",
    "Yuri Lima"
  ],
  "comment": "18 pages, 2 figures",
  "categories": [
    "math.DS",
    "math.CO",
    "math.PR"
  ],
  "abstract": "We study P\\'olya urns on hypergraphs and prove that, when the incidence matrix of the hypergraph is injective, there exists a point $v=v(H)$ such that the random process converges to $v$ almost surely. We also provide a partial result when the incidence matrix is not injective.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-09-29T21:49:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pólya urns",
      "hypergraph",
      "incidence matrix",
      "study polya urns",
      "random process converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}