{"paper":{"title":"R\\'enyi entropy power inequality and a reverse","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"math.PR","authors_text":"Jiange Li","submitted_at":"2017-04-09T17:46:12Z","abstract_excerpt":"This paper is twofold. In the first part, we present a refinement of the R\\'enyi Entropy Power Inequality (EPI) recently obtained in \\cite{BM16}. The proof largely follows the approach in \\cite{DCT91} of employing Young's convolution inequalities with sharp constants. In the second part, we study the reversibility of the R\\'enyi EPI, and confirm a conjecture in \\cite{BNT15, MMX16} in two cases. Connections with various $p$-th mean bodies in convex geometry are also explored."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.02634","kind":"arxiv","version":2},"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"}