{
  "abstract": "We establish an a priori bound for the dynamical parabolic $Φ_3^4$ model with harmonic potential. This bound yields the global well-posedness of the equation and, via the Krylov-Bogoliubov method, the existence of an invariant measure, shown to be non-Gaussian. The argument builds on the strategy developed by Mourrat and Weber for the periodic $Φ_3^4$ model, with substantial modifications to handle the non-compact geometry of $\\mathbb{R}^3$ and the spectral framework imposed by the harmonic oscillator. We further prove that this measure is unique in the small-coupling regime.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12026",
  "author_total": 3,
  "authors": [
    {
      "name": "Aurélien Deya"
    },
    {
      "name": "Reika Fukuizumi"
    },
    {
      "name": "Laurent Thomann"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/079w3j0c5h4w3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12026",
  "fulltext_url": null,
  "id": "079w3j0c5h4w3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12026",
  "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.AP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Advanced Mathematical Physics Problems"
    ]
  ],
  "openalex": "W7212887026",
  "pdf_url": "https://arxiv.org/pdf/2609.12026",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/079w3j0c5h4w3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:11Z",
      "native_id": "2609.12026",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12026"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "On the parabolic $Φ_3^4$ model for the harmonic oscillator II: global existence and invariant measures",
  "title_text": "On the parabolic Φ_3^4 model for the harmonic oscillator II: global existence and invariant measures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/079w3j0c5h4w3",
  "venue": "arXiv",
  "versions": []
}