{"paper":{"title":"Lift zonoid order and functional inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexei M. Kulik, Taras D. Tymoshkevych","submitted_at":"2013-08-10T14:14:23Z","abstract_excerpt":"We introduce the notion of a weighted lift zonoid and show that, for properly chosen weights v, the ordering condition on a measure \\mu, formulated in terms of the weighted lift zonoids of this measure, leads to certain functional inequalities for this measure, such as non-linear extensions of Bobkov's shift inequality and weighted inverse log-Sobolev inequality. The choice of the weight K, involved in our version of the inverse log-Sobolev inequality, differs substantially from those available in the literature, and requires the weight v, involved into the definition of the weighted lift zono"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.2320","kind":"arxiv","version":4},"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"}