{"paper":{"title":"Poincar\\'e inequality 3/2 on the Hamming cube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexander Volberg, Paata Ivanisvili","submitted_at":"2016-08-13T19:39:23Z","abstract_excerpt":"For any $n \\geq 1$, and any $f :\\{-1,1\\}^{n} \\to \\mathbb{R}$ we have $ \\Re\\, \\mathbb{E}\\, (f + i\\, |\\nabla f|)^{3/2} \\leq \\Re\\, (\\mathbb{E}f)^{3/2}, $ where $z^{3/2}$ for $z=x+iy$ is taken with principal branch and $\\Re$ denotes the real part."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.04021","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"}