{"paper":{"title":"Improving constant in end-point Poincar\\'e inequality on Hamming cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.PR","authors_text":"Alexander Volberg, Dong Li, Paata Ivanisvili, Ramon van Handel","submitted_at":"2018-11-14T01:16:29Z","abstract_excerpt":"We improve the constant $\\frac{\\pi}{2}$ in $L^1$-Poincar\\'e inequality on Hamming cube. For Gaussian space the sharp constant in $L^1$ inequality is known, and it is $\\sqrt{\\frac{\\pi}{2}}$. For Hamming cube the sharp constant is not known, and $\\sqrt{\\frac{\\pi}{2}}$ gives an estimate from below for this sharp constant. On the other hand, L. Ben Efraim and F. Lust-Piquard have shown an estimate from above: $C_1\\le \\frac{\\pi}{2}$. There are at least two other independent proofs of the same estimate from above (we write down them in this note). Since those proofs are very different from the proof"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05584","kind":"arxiv","version":5},"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"}