{
  "id": "2411.06195",
  "version": "v1",
  "published": "2024-11-09T14:33:58.000Z",
  "updated": "2024-11-09T14:33:58.000Z",
  "title": "Restrictions of some reinforced processes to subgraphs",
  "authors": [
    "Margherita Disertori",
    "Franz Merkl",
    "Silke W. W. Rolles"
  ],
  "comment": "30 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the restriction of the vertex-reinforced jump process to a subset of the vertex set is a mixture of vertex-reinforced jump processes. A similar statement holds for the non-linear hyperbolic supersymmetric sigma model. This is then applied to vertex-reinforced jump processes on subdivided versions of graphs of bounded degree, where every edge is replaced by a finite sequence of edges. We prove that discrete-time processes associated to suitable corresponding restrictions are mixtures of positive recurrent Markov chains. We also deduce a similar statement for edge-reinforced random walks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-11-09T14:33:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "60G60"
    ],
    "keywords": [
      "vertex-reinforced jump process",
      "reinforced processes",
      "restriction",
      "non-linear hyperbolic supersymmetric sigma model",
      "similar statement holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}