{
  "abstract": "We analyze the level lines of the Gaussian Free Field with logarithmic singularities in polygonal domains. We focus on the (none-zero) singular case and compare it to the singular-free setting. The law of the level lines for the field in singular case is absolutely continuous with respect to the law for the singular-free case, with a Radon-Nikodym derivative related to the reduced Green's energy which is introduced by F. Viklund and D. W. Nyström~[VN24]. These level lines admit a Brownian motion representation. In the singular-free case, such representation involves Poisson point processes of Brownian loops and excursions; while for the singular case, it additionally includes Poisson point processes of Brownian bubbles and bridges. The special cases of one or two singularities yield moment-generating functions of the conformal radius, which can be interpreted as one-point and two-point correlation functions of vertex operators in conformal field theory at the free-boson point. While the Radon-Nikodym derivative is bounded away from the singularities, the behavior of the level lines near the singularities is markedly different from the singular-free case, with different asymptotic probabilities for all level lines to remain close to the singularity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07272",
  "author_total": 3,
  "authors": [
    {
      "name": "Mingchang Liu"
    },
    {
      "name": "Titus Lupu"
    },
    {
      "name": "Hao Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2jm30qbcwjvtr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07272",
  "fulltext_url": null,
  "id": "2jm30qbcwjvtr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07272",
  "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": "W7221025666",
  "pdf_url": "https://arxiv.org/pdf/2610.07272",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2jm30qbcwjvtr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:22Z",
      "native_id": "2610.07272",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07272"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Gaussian free field with logarithmic singularities and reduced Green's energy",
  "title_text": "Gaussian free field with logarithmic singularities and reduced Green's energy",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/2jm30qbcwjvtr",
  "venue": "arXiv",
  "versions": []
}