{
  "abstract": "In a spiked covariance model, let $\\mathcal{H}$ and $\\mathcal{B}$ be selected sample and population eigenvector matrices. Their alignment matrix $Ξ=\\mathcal{H}^\\top\\mathcal{B}$ is a latent oracle diagnostic of direction-specific correspondence beyond subspace overlap. We study its uniform pathwise recovery in a nested high-dimensional, low-sample-size experiment with fixed sample size and growing dimension. At every fixed model, an observable spectral contrast consistently estimates the row Gram matrix $ΞΞ^\\top$. For two or more spikes, however, no measurable estimator sequence achieves uniformly reliable almost-sure path recovery of $Ξ$ over a family having common spike strengths and a common signal subspace but different ordered eigenframes. For every $0<ε<1/\\sqrt{2}$, a finite orbit forces each estimator to have some orbit point at which the approximate path-recovery probability is at most a variational bound $u(ε)$, where $u(ε)$ tends to zero as $ε$ tends to zero. The worst-model exact-recovery probability over a countable orbit is zero. Thus the Gram summary is recoverable model by model, while the full alignment matrix is not uniformly recoverable along the nested path.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23081",
  "author_total": 2,
  "authors": [
    {
      "name": "Hubeyb Gurdogan"
    },
    {
      "name": "Alex Shkolnik"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d57kvzahtvpsq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23081",
  "fulltext_url": null,
  "id": "d57kvzahtvpsq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23081",
  "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.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214022375",
  "pdf_url": "https://arxiv.org/pdf/2609.23081",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d57kvzahtvpsq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23081",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23081"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Recovery Limits for Eigenvector Alignment in HDLSS Spiked Covariance Models",
  "title_text": "Recovery Limits for Eigenvector Alignment in HDLSS Spiked Covariance Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:33Z",
  "url": "https://research.draconitic.com/paper/d57kvzahtvpsq",
  "venue": "arXiv",
  "versions": []
}