{
  "abstract": "In this paper, we study the large deviation principle (LDP) for a tensor-weighted functional of i.i.d. random variables, when the sequence of tensors converges under a variant of the \"bad\" cut norm. Using the LDP, we analyze a Gibbs measure with a tensor-valued Hamiltonian, and characterize the optimizers of the limiting variational problem in terms of a functional fixed point equation. As applications, we focus on several concrete examples, which include monochromatic subgraph counts in sparse random graphs, Erdős-Rényi hypergraphs, and a generalized Potts statistic of order $v\\ge 2$. Studying the optimization problem, we give sufficient conditions for uniqueness of the optimizer, as well as for existence of constant optimizers (replica symmetry). Our results demonstrate universal weak laws for a large class of tensor Gibbs models with approximately regular tensors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02682",
  "author_total": 4,
  "authors": [
    {
      "name": "Reihaneh Malekian"
    },
    {
      "name": "Sohom Bhattacharya"
    },
    {
      "name": "Nabarun Deb"
    },
    {
      "name": "Sumit Mukherjee"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6qsj8qqzjggdy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02682",
  "fulltext_url": null,
  "id": "6qsj8qqzjggdy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02682",
  "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": "W7207851285",
  "pdf_url": "https://arxiv.org/pdf/2609.02682",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6qsj8qqzjggdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:20Z",
      "native_id": "2609.02682",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02682"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "LDP for Tensor Forms",
  "title_text": "LDP for Tensor Forms",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:20Z",
  "url": "https://research.draconitic.com/paper/6qsj8qqzjggdy",
  "venue": "arXiv",
  "versions": []
}