{"paper":{"title":"Asymptotic shape of the convex hull of isotropic log-concave random vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Antonis Tsolomitis, Apostolos Giannopoulos, Labrini Hioni","submitted_at":"2016-01-10T19:00:05Z","abstract_excerpt":"Let $x_1,\\ldots ,x_N$ be independent random points distributed according to an isotropic log-concave measure $\\mu $ on ${\\mathbb R}^n$, and consider the random polytope $$K_N:={\\rm conv}\\{ \\pm x_1,\\ldots ,\\pm x_N\\}.$$ We provide sharp estimates for the querma\\ss{}integrals and other geometric parameters of $K_N$ in the range $cn\\ls N\\ls\\exp (n)$; these complement previous results from \\cite{DGT1} and \\cite{DGT} that were given for the range $cn\\ls N\\ls\\exp (\\sqrt{n})$. One of the basic new ingredients in our work is a recent result of E.~Milman that determines the mean width of the centroid bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02252","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"}