{
  "abstract": "We prove that, on a Galton-Watson tree with almost surely finite offspring and infinite offspring mean, the random interchange process has critical parameter zero for infinite cycles, conditionally on survival. Combined with the finite-mean strict inequality established in \\emph{arXiv:2503.03319}, this gives a dichotomy for locally finite Galton-Watson trees with offspring mean in $(1,\\infty]$: the loop and link critical parameters coincide exactly in the infinite-mean case. The proof reduces the tree problem to a finite permutation estimate derived from peeling estimates for random surfaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08149",
  "author_total": 3,
  "authors": [
    {
      "name": "Andreas Klippel"
    },
    {
      "name": "Benjamin Lees"
    },
    {
      "name": "Christian Mönch"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6w6bx5d4p8mbf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08149",
  "fulltext_url": null,
  "id": "6w6bx5d4p8mbf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08149",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7220903695",
  "pdf_url": "https://arxiv.org/pdf/2610.08149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6w6bx5d4p8mbf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.08149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Infinite-mean Galton-Watson trees have zero random-interchange threshold",
  "title_text": "Infinite-mean Galton-Watson trees have zero random-interchange threshold",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/6w6bx5d4p8mbf",
  "venue": "arXiv",
  "versions": []
}