{"paper":{"title":"A short proof of Paouris' inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Alain Pajor, Alexander E. Litvak, Krzysztof Oleszkiewicz, Nicole Tomczak-Jaegermann, Rados{\\l}aw Adamczak, Rafa{\\l} Lata{\\l}a","submitted_at":"2012-05-11T13:14:26Z","abstract_excerpt":"We give a short proof of a result of G. Paouris on the tail behaviour of the Euclidean norm $|X|$ of an isotropic log-concave random vector $X\\in\\R^n$, stating that for every $t\\geq 1$, $P(|X|\\geq ct\\sqrt n)\\leq \\exp(-t\\sqrt n)$. More precisely we show that for any log-concave random vector $X$ and any $p\\geq 1$, $(E|X|^p)^{1/p}\\sim E |X|+\\sup_{z\\in S^{n-1}}(E |< z,X>|^p)^{1/p}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2515","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"}