{
  "abstract": "We establish a maximum-variance inequality for discrete $α$-concave random variables in the regime $-1/3<α<0$, extending corresponding results beyond the discrete log-concave setting. As applications, we obtain a reverse entropy power inequality and bounds for the Lévy concentration function. We further establish polynomial-type concentration inequalities, reflecting the heavy-tailed nature of the class. A main tool in our approach is a convex majorization principle that reduces the relevant extremal problems to suitable $α$-affine distributions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05439",
  "author_total": 3,
  "authors": [
    {
      "name": "Abdulmajeed Alqasem"
    },
    {
      "name": "Heshan Aravinda"
    },
    {
      "name": "Arnaud Marsiglietti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j8sbdypxx9rx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05439",
  "fulltext_url": null,
  "id": "1j8sbdypxx9rx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05439",
  "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",
      "2604|Mathematical Inequalities and Applications"
    ]
  ],
  "openalex": "W7220681719",
  "pdf_url": "https://arxiv.org/pdf/2610.05439",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j8sbdypxx9rx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05439",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05439"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Majorization, Entropy and Concentration Inequalities for Discrete $α$-Concave Random Variables",
  "title_text": "Majorization, Entropy and Concentration Inequalities for Discrete α-Concave Random Variables",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/1j8sbdypxx9rx",
  "venue": "arXiv",
  "versions": []
}