{
  "abstract": "Power-law eigenvalue spectra of covariance matrices estimated from data appear in diverse domains ranging from neural populations to proteins. We introduce a generative latent feature model for such data, optionally corrupted by measurement noise, and develop its spectral theory. We derive closed leading-order self-consistent equations for the Stieltjes transform of the covariance matrix from which the bulk eigenvalue density is obtained and provide a variational principle for the self-consistent equations. We also compute the positions and fluctuations of isolated top eigenvalues. The theory is validated in known algebraic limits and tested against simulations.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39013",
  "author_total": 1,
  "authors": [
    {
      "name": "Philipp Fleig"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84td7yz318rpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39013",
  "fulltext_url": null,
  "id": "84td7yz318rpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39013",
  "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",
      "cond-mat.dis-nn"
    ],
    [
      "arxiv",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "physics.data-an"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39013",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84td7yz318rpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39013",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39013"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.dis-nn",
      "subfield": "condensed-matter"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Spectral theory of large data with power-law latent features",
  "title_text": "Spectral theory of large data with power-law latent features",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/84td7yz318rpc",
  "venue": "arXiv",
  "versions": []
}