{
  "abstract": "In this paper, we study fluctuations of fixed subgraph counts in dense exponential random graphs on $n$ vertices. We compare each normalized subgraph count $V$ with the normalized edge count $W$: their difference $V-W$ is $O(n^{-1/2})$ in $L^2$, whereas $\\mathbb{E}[(V-W)f(W)]=O(n^{-1})$ for every $1$-Lipschitz function $f$. We also obtain $O(n^{-1})$ Kolmogorov and Wasserstein bounds, optimal for the edge count, with relative variance error of the same order. These estimates hold uniformly on compact subsets of the ferromagnetic subcritical and absolute-coefficient Dobrushin regions, and under small fixed signed perturbations of the former. Using this uniform control, we derive a local Gaussian likelihood expansion with rank-one leading Fisher information and two-sided moderate deviations with an explicit cubic correction. The proofs combine two applications of the normal Stein equation, covariance estimates from Glauber dynamics and exponential tilting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28078",
  "author_total": 3,
  "authors": [
    {
      "name": "Hui-Lin Liu"
    },
    {
      "name": "Song-Hao Liu"
    },
    {
      "name": "Dawei Lu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ashc6n5s3dn6q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28078",
  "fulltext_url": null,
  "id": "ashc6n5s3dn6q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28078",
  "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": "W7223138425",
  "pdf_url": "https://arxiv.org/pdf/2610.28078",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ashc6n5s3dn6q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.28078",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28078"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fluctuations of subgraph counts in exponential random graphs",
  "title_text": "Fluctuations of subgraph counts in exponential random graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/ashc6n5s3dn6q",
  "venue": "arXiv",
  "versions": []
}