{"paper":{"title":"Intrinsic entropies of log-concave distributions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Varun Jog, Venkat Anantharam","submitted_at":"2017-02-03T23:36:33Z","abstract_excerpt":"The entropy of a random variable is well-known to equal the exponential growth rate of the volumes of its typical sets. In this paper, we show that for any log-concave random variable $X$, the sequence of the $\\lfloor n\\theta \\rfloor^{\\text{th}}$ intrinsic volumes of the typical sets of $X$ in dimensions $n \\geq 1$ grows exponentially with a well-defined rate. We denote this rate by $h_X(\\theta)$, and call it the $\\theta^{\\text{th}}$ intrinsic entropy of $X$. We show that $h_X(\\theta)$ is a continuous function of $\\theta$ over the range $[0,1]$, thereby providing a smooth interpolation between"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01203","kind":"arxiv","version":1},"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"}