{
  "abstract": "Kikuchi matrices are a family of structured matrices that were introduced to study problems involving tensors and hypergraphs. We show that, as the ambient dimension grows, dense random Kikuchi matrices have a limit described by a system of $Γ$-independent semicircular elements. This characterizes their limiting spectral distribution and yields improved bounds on their spectral norm, a key quantity in the analysis of algorithms for Tensor PCA. Finally, we show that, in an appropriate double limit, independent Kikuchi matrices converge to the $q$-Gaussian system, another central object in noncommutative probability.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.02008",
  "author_total": 5,
  "authors": [
    {
      "name": "Afonso S. Bandeira"
    },
    {
      "name": "Dmitriy Kunisky"
    },
    {
      "name": "Petar Nizić-Nikolac"
    },
    {
      "name": "Lucas Pesenti"
    },
    {
      "name": "Robert Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4g37g6629wx84.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.02008",
  "fulltext_url": null,
  "id": "4g37g6629wx84",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.02008",
  "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",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.OA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7216579641",
  "pdf_url": "https://arxiv.org/pdf/2610.02008",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4g37g6629wx84.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:07Z",
      "native_id": "2610.02008",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.02008"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.OA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence of Kikuchi matrices to $Γ$-independent and $q$-Gaussian limits",
  "title_text": "Convergence of Kikuchi matrices to Γ-independent and q-Gaussian limits",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:07Z",
  "url": "https://research.draconitic.com/paper/4g37g6629wx84",
  "venue": "arXiv",
  "versions": []
}