{"paper":{"title":"An asymptotically sharp form of Ball's inequality by probability methods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Susanna Spektor","submitted_at":"2017-08-27T16:45:49Z","abstract_excerpt":"To prove by probabilistic methods that every $(n-1)$-dimensional section of the unit cube in $R^n$ has volume at most $\\sqrt 2$, K.  Ball made essential use of the inequality $$ \\frac{1}{\\pi}\\int_{-\\infty}^{\\infty} \\left(\\frac{\\sin^2 t}{t^2}\\right)^pdt\\leq \\frac{\\sqrt 2}{\\sqrt p}, \\quad p\\geq 1, $$ in which equality holds if and only if $p=1$.\n  The right side of above inequality has the correct rate of decay though the limit of the ratio of the right to left side is ${\\sqrt{\\frac{3}{\\pi}}}$ rather then $\\sqrt 2$. Applying Ball's methods we put all of this into the improved form of the Ball's "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08106","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":""},"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"}