{"paper":{"title":"Sharp constants relating the sub-Gaussian norm and the sub-Gaussian parameter","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Lasse Leskel\\\"a, Matvei Zhukov","submitted_at":"2025-07-08T12:24:52Z","abstract_excerpt":"We determine the optimal constants in the classical inequalities relating the sub-Gaussian norm \\(\\|X\\|_{\\psi_2}\\) and the sub-Gaussian parameter \\(\\sigma_X\\) for centered real-valued random variables. We show that \\(\\sqrt{3/8} \\cdot \\|X\\|_{\\psi_2} \\le \\sigma_X \\le \\sqrt{\\log 2} \\cdot \\|X\\|_{\\psi_2}\\), and that both bounds are sharp, attained by the standard Gaussian and Rademacher distributions, respectively."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.05928","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2507.05928/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}