{"paper":{"title":"Intrinsic volumes of random polytopes with vertices on the boundary of a convex body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Daniel Hug, Ferenc Fodor, K\\'aroly J. B\\\"or\\\"oczky","submitted_at":"2011-03-25T14:22:31Z","abstract_excerpt":"Let $K$ be a convex body in $\\R^d$, let $j\\in\\{1, ..., d-1\\}$, and let $\\varrho$ be a positive and continuous probability density function with respect to the $(d-1)$-dimensional Hausdorff measure on the boundary $\\partial K$ of $K$. Denote by $K_n$ the convex hull of $n$ points chosen randomly and independently from $\\partial K$ according to the probability distribution determined by $\\varrho$. For the case when $\\partial K$ is a $C^2$ submanifold of $\\R^d$ with everywhere positive Gauss curvature, M. Reitzner proved an asymptotic formula for the expectation of the difference of the $j$th int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4978","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"}