{
  "abstract": "Let $\\varepsilon_1,\\ldots,\\varepsilon_n$ be independent Rademacher random variables. We settle the best constant $c$ such that \\[ \\mathbb{E}\\Bigl|\\sum_{j=1}^n a_j\\varepsilon_j\\Bigr| \\ge \\frac{1}{\\sqrt{2}} +c\\Bigl|a-\\frac{e_1+e_2}{\\sqrt{2}}\\Bigr| \\] holds for every $n\\ge 2$ and every unit vector $a\\in\\mathbb{R}^n$ with $a_1\\ge\\cdots\\ge a_n\\ge 0$. We prove that the optimal constant is $c=(2-\\sqrt{2})^{3/2}/8$, with equality attained at $a=\\frac{1}{2}(1,1,1,1,0,\\ldots,0)$ for $n\\ge 4$. This completes a line of research by De-Diakonikolas-Servedio, Eskenazis-Nayar-Tkocz and Fang-Wang.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.07526",
  "author_total": 1,
  "authors": [
    {
      "name": "Xinyuan Xie"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cpk9bj2y4jknp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.07526",
  "fulltext_url": null,
  "id": "cpk9bj2y4jknp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.07526",
  "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.FA"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Probability and Statistical Research"
    ]
  ],
  "openalex": "W7221044908",
  "pdf_url": "https://arxiv.org/pdf/2610.07526",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cpk9bj2y4jknp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.07526",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.07526"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stability of Szarek's inequality with best constant",
  "title_text": "Stability of Szarek's inequality with best constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/cpk9bj2y4jknp",
  "venue": "arXiv",
  "versions": []
}