{
  "abstract": "We study multi-excited random walks on infinite locally finite trees. The model is described by placing a stack of ``cookies'' at each vertex, with one cookie consumed on each successive visit. As long as cookies remain, the walk is in an excited regime and makes nearest-neighbour steps according to a prescribed sequence of biases. Once the stack is exhausted, the walk is in a non-excited regime and moves uniformly among the neighbouring vertices. The model is closely connected to foraging ecology, where repeated visits to a location can deplete local resources and thereby influence the attractiveness of that location for future visits. We prove that the process exhibits a sharp phase transition between recurrence and transience. The critical threshold is determined by the branching-ruin number of the tree, which is equal to the Hausdorff dimension of the tree's boundary under a suitable metric. Our result substantially extends Zerner's recurrence-transience criterion for multi-excited random walks on $\\mathbb Z$ [Probab. Theory Related Fields 133 (2005)] to general trees.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40084",
  "author_total": 2,
  "authors": [
    {
      "name": "Jack Mills"
    },
    {
      "name": "Tuan-Minh Nguyen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9c1q2ff682x07.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40084",
  "fulltext_url": null,
  "id": "9c1q2ff682x07",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40084",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40084",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9c1q2ff682x07.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.40084",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40084"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Multi-excited random walks on general trees",
  "title_text": "Multi-excited random walks on general trees",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/9c1q2ff682x07",
  "venue": "arXiv",
  "versions": []
}