{
  "abstract": "The Free $\\mathbf{w}$-Maximal Spanning Forest (FMaxSF) is a weighted generalization of the classical Free Minimal Spanning Forest (FMSF) that is able to detect nonhyperfiniteness in percolation on nonunimodular graphs. We introduce a parameterized family of invariant random spanning forests that interpolates between these models. For every finite positive value of the parameter $β$, the construction retains many of the desired properties of FMaxSF while also admitting the finite-subtree forcing property of FMSF. We study local limits of these forests and, in particular, show that the small-$β$ limit of the wired variant coincides with FMSF if and only if $p_h=p_u$, where $p_h$ is the threshold for the existence of heavy clusters and $p_u$ is the uniqueness threshold for Bernoulli$(p)$ percolation. Finally, we show that the Free and the Wired $\\mathbf{w}$-Maximal Spanning Forests may coincide even if $p_h<p_u$, providing a negative answer to a question of Terlov and Timár.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.11845",
  "author_total": 3,
  "authors": [
    {
      "name": "Shirshendu Chatterjee"
    },
    {
      "name": "Yang Chen"
    },
    {
      "name": "Grigory Terlov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bn745sg85ybmz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.11845",
  "fulltext_url": null,
  "id": "bn745sg85ybmz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.11845",
  "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",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212307557",
  "pdf_url": "https://arxiv.org/pdf/2609.11845",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bn745sg85ybmz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:30Z",
      "native_id": "2609.11845",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.11845"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "$β$-Skewed Maximal Spanning Forests",
  "title_text": "β-Skewed Maximal Spanning Forests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:30Z",
  "url": "https://research.draconitic.com/paper/bn745sg85ybmz",
  "venue": "arXiv",
  "versions": []
}