{"paper":{"title":"On Renyi Entropy Power Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"Eshed Ram, Igal Sason","submitted_at":"2016-01-25T10:56:38Z","abstract_excerpt":"This paper gives improved R\\'{e}nyi entropy power inequalities (R-EPIs). Consider a sum $S_n = \\sum_{k=1}^n X_k$ of $n$ independent continuous random vectors taking values on $\\mathbb{R}^d$, and let $\\alpha \\in [1, \\infty]$. An R-EPI provides a lower bound on the order-$\\alpha$ R\\'enyi entropy power of $S_n$ that, up to a multiplicative constant (which may depend in general on $n, \\alpha, d$), is equal to the sum of the order-$\\alpha$ R\\'enyi entropy powers of the $n$ random vectors $\\{X_k\\}_{k=1}^n$. For $\\alpha=1$, the R-EPI coincides with the well-known entropy power inequality by Shannon. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.06555","kind":"arxiv","version":3},"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"}