{"paper":{"title":"On reverse hypercontractivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.FA"],"primary_cat":"math.PR","authors_text":"Arnab Sen, Elchanan Mossel, Krzysztof Oleszkiewicz","submitted_at":"2011-08-04T20:33:38Z","abstract_excerpt":"We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new comparison lemma for Dirichlet forms and an extension of the Strook-Varapolos inequality.\n  A consequence of our analysis is that {\\em all} simple operators $L=Id-\\E$ as well as their tensors satisfy uniform reverse hypercontractive inequalities. That is, for all $q<p<1$ and every positive valued function $f$ for $t \\geq \\log \\frac{1-q}{1-p}$ we have $\\| e^{-tL}f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.1210","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"}