{
  "abstract": "Classical central limit theorems (CLTs) for log-partition functions of Ising models on Erdős-Rényi random graphs lead to degenerate limits in the high-temperature regime when self-loops are absent. In this paper, we fill this surprising gap in the more general context of Ising models on inhomogeneous random graphs. In particular, we show that if $G(N,W)$ is an inhomogeneous random graph without self-loops generated by a graphon $W$, then, in the high-temperature regime, the log-partition function of the corresponding Ising model satisfies a CLT on the $N$-scale, with a limiting variance that incorporates contributions from cycles of all orders. This behavior contrasts sharply with that of the corresponding model in which self-loops are allowed, where the analogous Gaussian fluctuations occur on the $\\sqrt{N}$-scale, with their asymptotic variance determined entirely by the diagonal profile of $W$. Our analysis yields, as a byproduct of independent interest, a CLT for the log-determinant of the associated resolvent matrix, established by combining the Lindeberg CLT for triangular arrays with suitable bounds on higher-order trace terms.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.01298",
  "author_total": 2,
  "authors": [
    {
      "name": "Sanchayan Bhowal"
    },
    {
      "name": "Somabha Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7z6hr2cf0w5x0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.01298",
  "fulltext_url": null,
  "id": "7z6hr2cf0w5x0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.01298",
  "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": "W7216405892",
  "pdf_url": "https://arxiv.org/pdf/2610.01298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7z6hr2cf0w5x0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.01298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.01298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Higher-Order Fluctuations of the Log-Partition Function for Ising Models on Inhomogeneous Random Graphs",
  "title_text": "Higher-Order Fluctuations of the Log-Partition Function for Ising Models on Inhomogeneous Random Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/7z6hr2cf0w5x0",
  "venue": "arXiv",
  "versions": []
}