{"paper":{"title":"Notes on constants for maxima of Rademacher averages","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Woonyoung Chang","submitted_at":"2026-06-29T14:58:24Z","abstract_excerpt":"Let $\\epsilon_{ij}, i,j\\geq 1$ be independent Rademacher variables. We prove \\begin{equation*} \\mathbb{E} \\max_{1\\leq j\\leq p}\\left|\\frac{1}{n}\\sum_{i=1}^n\\epsilon_{ij}\\right| \\geq \\min\\left\\{\\frac{255}{256},\\frac{1}{\\sqrt{2\\log 2}}\\sqrt{\\frac{\\log(2p)}{n}}\\right\\}. \\end{equation*} The equality is attained, for instance, by $(n,p)=(2,1)$ and $(n,p)=(2,8).$ We also discuss the optimality of the numerical constants."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.30411","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/2606.30411/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"}