{
  "abstract": "For the sinh-Gordon model (without external mass term), we show that the log-Sobolev inequality holds uniformly in the lattice and volume regularisations for all parameters in the regime in which the Gaussian multiplicative chaos has second moments. This implies that infinite-volume ``massless'' sinh-Gordon measures on $\\mathbb{R}^2$ satisfying all Osterwalder--Schrader axioms exist and that they have exponential decay of correlations (are ``massive''). The proof uses the Polchinski equation method for log-Sobolev inequalities. The required estimates on the renormalised potential are established using simple perturbation theoretic bounds, valid for absolutely monotone potentials, and an extension of the correlation inequality of Ding--Song--Sun to potentials in the GHS class. This inequality is proved also by using a variant of the Polchinski equation through the maximum principle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28091",
  "author_total": 4,
  "authors": [
    {
      "name": "Omar Abdelghani"
    },
    {
      "name": "Roland Bauerschmidt"
    },
    {
      "name": "Thierry Bodineau"
    },
    {
      "name": "Benoit Dagallier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8689bdre3a0jd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28091",
  "fulltext_url": null,
  "id": "8689bdre3a0jd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28091",
  "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": "W7214242016",
  "pdf_url": "https://arxiv.org/pdf/2609.28091",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8689bdre3a0jd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.28091",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28091"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Log-Sobolev inequality for the sinh-Gordon model",
  "title_text": "Log-Sobolev inequality for the sinh-Gordon model",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/8689bdre3a0jd",
  "venue": "arXiv",
  "versions": []
}