{"paper":{"title":"On the geometry of random convex sets between polytopes and zonotopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.MG","authors_text":"David Alonso-Guti\\'errez, Joscha Prochno","submitted_at":"2016-07-31T18:10:19Z","abstract_excerpt":"In this work we study a class of random convex sets that \"interpolate\" between polytopes and zonotopes. These sets arise from considering a $q^{th}$-moment ($q\\geq 1$) of an average of order statistics of $1$-dimensional marginals of a sequence of $N\\geq n$ independent random vectors in $\\mathbb R^n$. We consider the random model of isotropic log-concave distributions as well as the uniform distribution on an $\\ell_p^n$-sphere ($1\\leq p < \\infty$) with respect to the cone probability measure, and study the geometry of these sets in terms of the support function and mean width. We provide asymp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.00830","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"}