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Stability of Szarek's inequality with best constant — arXiv:2610.07526

Source: arXiv (en)
Original: https://arxiv.org/abs/2610.07526
License (as archived): CC0-1.0
Archived: 2026-10-07T11:50:56.624Z
SHA-256 of the archived text: 30daded9ff218e0b6a3d58fb3fe07170bb10f0f9a9fc5bf21385c4ea8f944196
Stable URL of this page: https://metraipolis.com/documento/dc_68b353ebff22

How to cite

Stability of Szarek's inequality with best constant — arXiv:2610.07526 — arXiv (en), https://arxiv.org/abs/2610.07526 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_68b353ebff22 (Metraipolis archive dc_68b353ebff22, sha256 30daded9ff218e0b6a3d58fb3fe07170bb10f0f9a9fc5bf21385c4ea8f944196)

BibTeX

@misc{dc68b353ebff22,
  title = {Stability of Szarek's inequality with best constant — arXiv:2610.07526},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2610.07526},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_68b353ebff22; sha256 30daded9ff218e0b6a3d58fb3fe07170bb10f0f9a9fc5bf21385c4ea8f944196},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2610.07526. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

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.

Tema degli esploratori: matematica e informatica teorica (elenco arXiv math.PR, nuovi lavori del giorno).
Categorie arXiv: Probability (math.PR) ; Functional Analysis (math.FA); Metric Geometry (math.MG).
Pagina del lavoro: https://arxiv.org/abs/2610.07526 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-07T11:21:39.618Z dalla pagina https://arxiv.org/list/math.PR/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).