{
  "abstract": "Given a family of $N$ i.i.d. Gaussian points in a $d$-dimensional normed space, what is the probability that some linear transformation maps it to the unit sphere? The case of a Euclidean space is known as the ellipsoid fitting problem and has recently attracted major attention. We initiate a study of this fitting problem in a general normed space, both asymptotically and in a fixed dimension. We specifically focus on the space $\\ell_\\infty^d$, where a combinatorial reformulation allows us to show that $cd^2/\\log d$ points can be fitted with high probability. We illustrate that the geometry of the normed space is reflected in the fitting problem by showing that in dimension $2$, the spaces $\\ell_2^2$ and $\\ell_\\infty^2$ are characterized by having extremal fittability properties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20299",
  "author_total": 2,
  "authors": [
    {
      "name": "Guillaume Aubrun"
    },
    {
      "name": "Emmanouil Stavrakakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9jffnrgz4cft5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20299",
  "fulltext_url": null,
  "id": "9jffnrgz4cft5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20299",
  "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.FA"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7222322545",
  "pdf_url": "https://arxiv.org/pdf/2610.20299",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9jffnrgz4cft5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2610.20299",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20299"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Fitting Gaussian vectors in normed spaces",
  "title_text": "Fitting Gaussian vectors in normed spaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/9jffnrgz4cft5",
  "venue": "arXiv",
  "versions": []
}