{
  "abstract": "Subspace-valued data arise in dimension reduction, image-set and video recognition, and signal processing, and the Fréchet mean is their standard sample mean [11,9,15,23]. We establish a central limit theorem for the intrinsic sample Fréchet mean of i.i.d. observations on the real Grassmann manifold $\\mathrm{Gr}(p,n)$, as a specialization of the general theorem of [18]. Unlike prior results which require the distribution to vanish or place negligible mass near the cut locus of the population mean, we allow a continuous, possibly positive density. To enable our results, we derive two properties of $\\mathrm{Gr}(p,n)$: the first is that the union of the cut loci of all points within distance $δ$ of the mean has volume $O(δ)$. The second is that the Hessian of the squared distance function is integrable. We also give a smooth density on $\\mathrm{Gr}(1,2)$ for which the mean is unique but the Fréchet Hessian vanishes.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.24159",
  "author_total": 3,
  "authors": [
    {
      "name": "Bipayan Banerjee"
    },
    {
      "name": "Imon Banerjee"
    },
    {
      "name": "Swagatam Das"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/004z6eg4mnv5c.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.24159",
  "fulltext_url": null,
  "id": "004z6eg4mnv5c",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.24159",
  "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"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
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  ],
  "openalex": "W7223062811",
  "pdf_url": "https://arxiv.org/pdf/2610.24159",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/004z6eg4mnv5c.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.24159",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.24159"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "A Central Limit Theorem for Intrinsic Fréchet Means on Real Grassmannians",
  "title_text": "A Central Limit Theorem for Intrinsic Fréchet Means on Real Grassmannians",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:35Z",
  "url": "https://research.draconitic.com/paper/004z6eg4mnv5c",
  "venue": "arXiv",
  "versions": []
}