{"ID":2897018,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.05928","arxiv_id":"2507.05928","title":"Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter","abstract":"We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm \\(\\|X\\|_{ψ_2}\\) and the sub-Gaussian parameter \\(σ_X\\) for centered real-valued random variables. We show that \\(\\sqrt{3/8} \\cdot \\|X\\|_{ψ_2} \\le σ_X \\le \\sqrt{\\log 2} \\cdot \\|X\\|_{ψ_2}\\), and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively.","short_abstract":"We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm \\(\\|X\\|_{ψ_2}\\) and the sub-Gaussian parameter \\(σ_X\\) for centered real-valued random variables. We show that \\(\\sqrt{3/8} \\cdot \\|X\\|_{ψ_2} \\le σ_X \\le \\sqrt{\\log 2} \\cdot \\|X\\|_{ψ_2}\\), and that both bounds are sharp, att...","url_abs":"https://arxiv.org/abs/2507.05928","url_pdf":"https://arxiv.org/pdf/2507.05928v1","authors":"[\"Lasse Leskelä\",\"Matvei Zhukov\"]","published":"2025-07-08T12:24:52Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}