{
  "id": "2305.07359",
  "version": "v1",
  "published": "2023-05-12T10:09:44.000Z",
  "updated": "2023-05-12T10:09:44.000Z",
  "title": "Transience of vertex-reinforced jump processes with long-range jumps",
  "authors": [
    "Margherita Disertori",
    "Franz Merkl",
    "Silke W. W. Rolles"
  ],
  "comment": "38 pages, 6 figures",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We show that the vertex-reinforced jump process on the d-dimensional lattice with long-range jumps is transient as long as the initial weights do not decay too fast. The main ingredients in the proof are: the relation of the corresponding random environment on finite boxes with a non-linear supersymmetric hyperbolic sigma model, a comparison with a hierarchical model, and the translation of the hierarchical model to a non-homogeneous effective one-dimensional model.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-05-12T10:09:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K37",
      "60G60"
    ],
    "keywords": [
      "vertex-reinforced jump process",
      "long-range jumps",
      "non-linear supersymmetric hyperbolic sigma model",
      "transience",
      "hierarchical model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}