{
  "abstract": "We prove local laws for the resolvents of separable covariance matrices of the form $\\mathcal Q=A^{1/2}XBX^*A^{1/2}$, where $X=(x_{ij})$ is a $p\\times n$ random matrix whose entries $x_{ij}$ are i.i.d.~random variables with mean 0 and variance $n^{-1}$, and $A,B$ are deterministic non-negative definite symmetric (or Hermitian) matrices. Following the method developed in arXiv:1611.05364, we first establish a self-consistent equation for the resolvent of $\\mathcal Q$ and use it to prove optimal local laws without the technical assumption $\\mathbb{E}[x_{ij}^{3}]=0$, which was essential in the previous derivation of the local laws in arXiv:1809.04572. As an application of our local law, we compute the asymptotic distribution of the outlier eigenvalues for spiked separable covariance matrices, extending the corresponding result in arXiv:2008.11903.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29872",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhili Wang"
    },
    {
      "name": "Bin Qin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bbz9y4rzx0e02.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29872",
  "fulltext_url": null,
  "id": "bbz9y4rzx0e02",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29872",
  "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",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7204954177",
  "pdf_url": "https://arxiv.org/pdf/2608.29872",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bbz9y4rzx0e02.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29872",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29872"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Local Law and Outlier Eigenvalues of Spiked Separable Covariance Matrices",
  "title_text": "Local Law and Outlier Eigenvalues of Spiked Separable Covariance Matrices",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/bbz9y4rzx0e02",
  "venue": "arXiv",
  "versions": []
}