{
  "id": "2406.17344",
  "version": "v1",
  "published": "2024-06-25T07:58:30.000Z",
  "updated": "2024-06-25T07:58:30.000Z",
  "title": "Recurrence and transience for non-Archimedean and directed graphs",
  "authors": [
    "Matthias Keller",
    "Anna Muranova"
  ],
  "comment": "21 pages, 5 figures",
  "categories": [
    "math.CO",
    "math-ph",
    "math.AP",
    "math.MP",
    "math.PR",
    "math.SP"
  ],
  "abstract": "We introduce the notion of recurrence and transience for graphs over non-Archimedean ordered field. To do so we relate these graphs to random walks of directed graphs over the reals. In particular, we give a characterization of the real directed graphs which can arise is such a way. As a main result, we give characterization for recurrence and transience in terms of a quantity related to the capacity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-25T07:58:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "05C22",
      "31C20",
      "47S10",
      "05C50",
      "12J15",
      "47N30"
    ],
    "keywords": [
      "recurrence",
      "transience",
      "main result",
      "non-archimedean ordered field",
      "characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}