{
  "abstract": "The log-correlated Gaussian field (LGF) on $\\mathbb{R}^d$ ($d \\geq 2$) is a centered Gaussian random tempered distribution, defined modulo additive constants, whose covariance kernel is $\\log(1/|x-y|)$. In two dimensions, the LGF coincides with the whole-plane Gaussian Free Field (GFF). Because the field is a distribution, studying its pointwise behavior requires regularization via convolution with a mollifier. A point is called $α$-thick if the mollified field at that point grows like $α\\log(1/ε)$ as the mollification scale $ε\\to 0$. A natural question is whether the set of $α$-thick points depends on the choice of mollifier. We prove that for any two admissible mollifiers $ρ$ and $σ$ satisfying some mild conditions, the thick point sets coincide almost surely. The result holds in all dimensions $d \\geq 2$, and in the special case $d = 2$ extends to the zero-boundary GFF on any open domain with harmonically non-trivial boundary via the Markov property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.08132",
  "author_total": 1,
  "authors": [
    {
      "name": "Kyle Ambrose"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/52env24bzc9g4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.08132",
  "fulltext_url": null,
  "id": "52env24bzc9g4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.08132",
  "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": "W7211992578",
  "pdf_url": "https://arxiv.org/pdf/2609.08132",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/52env24bzc9g4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.08132",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.08132"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Thick points of log-correlated Gaussian fields do not depend on the mollifier",
  "title_text": "Thick points of log-correlated Gaussian fields do not depend on the mollifier",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/52env24bzc9g4",
  "venue": "arXiv",
  "versions": []
}