{"paper":{"title":"Maximal surface area of polytopes with respect to log-concave rotation invariant measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Galyna V. Livshyts","submitted_at":"2014-09-15T21:19:55Z","abstract_excerpt":"It was shown in \\cite{GL} that the maximal surface area of a convex set in $\\mathbb{R}^n$ with respect to a rotation invariant log-concave probability measure $\\gamma$ is of order $\\frac{\\sqrt{n}}{\\sqrt[4]{Var|X|} \\sqrt{\\mathbb{E}|X|}}$, where $X$ is a random vector in $\\mathbb{R}^n$ distributed with respect to $\\gamma$. In the present paper we discuss surface area of convex polytopes $P_K$ with $K$ facets. We find tight bounds on the maximal surface area of $P_K$ in terms of $K$. We show that $\\gamma(\\partial P_K)\\lesssim \\frac{\\sqrt{n}}{\\mathbb{E}|X|}\\cdot\\sqrt{\\log K}\\cdot\\log n$ for all $K"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4452","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"}