{
  "abstract": "In this paper, we introduce the coupled free energy $F_{-γ}^{\\rm cp}$ which is a natural generalization of the free energy functional defined by Berman. In the Fano case, our coupled free energy provides a diagonal approach to the coercivity of the coupled Ding functional. We also define the non-Archimedean coupled free energy $F_{-γ}^{\\rm cp,NA}$ on the space of finite energy measures on the Berkovich analytification. As a consequence of the regularization process of the non-Archimedean entropy established by Boucksom-Jonsson, Chi Li and Trusiani, we prove that the existence of a unique coupled Kähler-Einstein metric is equivalent to the stability condition that there exists $ε>0$ such that $F_{-1-ε}^{\\rm cp,NA} \\geq 0$ on the space of measures associated with a test configuration for the anticanonical line bundle. As a coupled version of the work by Berman, we show that the law of the empirical measure satisfies a large deviation principle whose rate function is the coupled free energy under the assumption that a conjecture by Hultgren is true. We also introduce a coupled version of the microscopic stability thresholds and prove that a uniformly coupled Gibbs stable Fano manifold has a unique coupled Kähler-Einstein metric. This is a generalization of the results by Fujita-Odaka and Berman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06968",
  "author_total": 2,
  "authors": [
    {
      "name": "Takahiro Aoi"
    },
    {
      "name": "Satoshi Nakamura"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/55xkafk8bcb23.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06968",
  "fulltext_url": null,
  "id": "55xkafk8bcb23",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06968",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.DG"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/55xkafk8bcb23.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:34Z",
      "native_id": "2611.06968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Coupled free energy and a diagonal approach to coupled Kähler-Einstein metrics",
  "title_text": "Coupled free energy and a diagonal approach to coupled Kähler-Einstein metrics",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:47Z",
  "url": "https://research.draconitic.com/paper/55xkafk8bcb23",
  "venue": "arXiv",
  "versions": []
}