{
  "abstract": "We consider the level sets of the Gaussian free field and the vacant set of random interlacements, both defined on a typical realization of the infinite cluster of supercritical Bernoulli bond percolation on $\\mathbb{Z}^d$, $d \\geq 3$. We prove that in the entire supercritical regime of Bernoulli bond percolation, both the level sets of the Gaussian free field and the vacant set of random interlacements undergo non-trivial percolation phase transitions at deterministic critical levels. A key aspect of the proof is the development of certain quenched controls over tree embeddings, permitting the application of a static renormalization scheme in the presence of spatial irregularities, which may be of independent interest.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08882",
  "author_total": 3,
  "authors": [
    {
      "name": "Alberto Chiarini"
    },
    {
      "name": "Zhizhou Liu"
    },
    {
      "name": "Maximilian Nitzschner"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ca7r86s0h0668.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08882",
  "fulltext_url": null,
  "id": "ca7r86s0h0668",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08882",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7212005252",
  "pdf_url": "https://arxiv.org/pdf/2609.08882",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ca7r86s0h0668.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:52Z",
      "native_id": "2609.08882",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08882"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters",
  "title_text": "Phase transition for strongly correlated percolation models on supercritical Bernoulli clusters",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:01Z",
  "url": "https://research.draconitic.com/paper/ca7r86s0h0668",
  "venue": "arXiv",
  "versions": []
}