{
  "abstract": "Let $n\\ge1$ and $1\\le p\\le2$, and let $X$ be uniformly distributed on the unit ball $B_p^n$ of $\\ell_p^n$. We prove that if $(a_1^2,\\ldots,a_n^2)$ majorizes $(b_1^2,\\ldots,b_n^2)$, then $\\langle b,X\\rangle^2$ is dominated by $\\langle a,X\\rangle^2$ in convex order. For $p<2$ this gives a nontrivial comparison of the complete squared-projection laws, whereas at $p=2$ it reduces to equality by rotational invariance. The result strengthens known majorization inequalities for individual power moments and provides a single distributional source for several familiar projection inequalities. Its proof combines a two-dimensional hinge-function comparison with a preservation theorem for Beta--Rademacher perturbations, which lifts elementary majorization transfers through the Dirichlet representation of the uniform measure on $B_p^n$. The comparison is stable under a common independent radial scaling and therefore extends to $\\ell_p$-radial measures with nonincreasing radial density. Consequences include simultaneous inequalities for moments, hinge functions, and Laplace transforms, together with Schur-convexity of Gaussian-regularized central-section densities. The range is sharp in the stated direction: for $p>2$, a support obstruction already occurs between a coordinate direction and a two-coordinate direction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.11451",
  "author_total": 1,
  "authors": [
    {
      "name": "Soufiane Fafe"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/583q9z54dj7sh.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.11451",
  "fulltext_url": null,
  "id": "583q9z54dj7sh",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.11451",
  "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",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7161065337",
  "pdf_url": "https://arxiv.org/pdf/2605.11451",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/583q9z54dj7sh.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2605.11451",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.11451"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convex order under majorization for projections of ell-p balls",
  "title_text": "Convex order under majorization for projections of ell-p balls",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/583q9z54dj7sh",
  "venue": "arXiv",
  "versions": []
}