{"paper":{"title":"The variance conjecture on some polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"David Alonso-Guti\\'errez, Jes\\'us Bastero","submitted_at":"2012-09-19T14:54:08Z","abstract_excerpt":"We show that any random vector uniformly distributed on any hyperplane projection of $B_1^n$ or $B_\\infty^n$ verifies the variance conjecture $$\\text{Var}|X|^2\\leq C\\sup_{\\xi\\in S^{n-1}}\\E<X,\\xi>^2\\E|X|^2.$$ Furthermore, a random vector uniformly distributed on a hyperplane projection of $B_\\infty^n$ verifies a negative square correlation property and consequently any of its linear images verifies the variance conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4270","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"}