{
  "abstract": "We study the empirical spectral distribution (ESD) of the random matrix $M_N=\\frac1N\\sum_{i=1}^N f(|πY_i|^2)\\,Y_iY_i^\\top$, where $π$ is a rank $k$ orthogonal projector on $\\R^p$, $Y_1,\\dots,Y_N$ are i.i.d. standard Gaussian vectors, and $k\\to \\infty$, $p/N\\to γ$. We here assume that $f(x)=g(x/k)$ for some function $g$ discontinuous at $x=1$. We show that the asymptotic ESD is characterized by a Marchenko--Pastur equation, independently of $k$. We also show that the result extends to sub Gaussian random vectors $Y_i$ and to the case where the projector is replaced with a more general weight $ϕ(Y_i)$. Last, in the Gaussian case, we study the emergence of outliers due to the weighting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40368",
  "author_total": 1,
  "authors": [
    {
      "name": "Sandrine Péché"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bkjtmcn6z8y3c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40368",
  "fulltext_url": null,
  "id": "bkjtmcn6z8y3c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40368",
  "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",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40368",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bkjtmcn6z8y3c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.40368",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40368"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Limiting ESD for a weighted sample covariance matrix",
  "title_text": "Limiting ESD for a weighted sample covariance matrix",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:51Z",
  "url": "https://research.draconitic.com/paper/bkjtmcn6z8y3c",
  "venue": "arXiv",
  "versions": []
}