{"paper":{"title":"Sharp Bounds Between Two R\\'enyi Entropies of Distinct Positive Orders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Ken-ichi Iwata, Yuta Sakai","submitted_at":"2016-04-29T20:21:25Z","abstract_excerpt":"Many axiomatic definitions of entropy, such as the R\\'enyi entropy, of a random variable are closely related to the $\\ell_{\\alpha}$-norm of its probability distribution. This study considers probability distributions on finite sets, and examines the sharp bounds of the $\\ell_{\\beta}$-norm with a fixed $\\ell_{\\alpha}$-norm, $\\alpha \\neq \\beta$, for $n$-dimensional probability vectors with an integer $n \\ge 2$. From the results, we derive the sharp bounds of the R\\'enyi entropy of positive order $\\beta$ with a fixed R\\'enyi entropy of another positive order $\\alpha$. As applications, we investig"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00019","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"}