{"paper":{"title":"On Dvoretzky's theorem for subspaces of $L_p$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.FA","authors_text":"Grigoris Paouris, Petros Valettas","submitted_at":"2015-10-25T19:06:21Z","abstract_excerpt":"We prove that for any $2<p<\\infty$ and for every $n$-dimensional subspace $X$ of $L_p$, represented on $\\mathbb R^n$, whose unit ball $B_X$ is in Lewis' position one has the following two-level Gaussian concentration inequality: \\[ \\mathbb P\\left( \\big| \\|Z\\| - \\mathbb E\\|Z\\| \\big| > \\varepsilon \\mathbb E\\|Z\\| \\right) \\leq C \\exp \\left (- c \\min \\left\\{ \\alpha_p \\varepsilon^2 n, (\\varepsilon n)^{2/p} \\right\\} \\right), \\quad 0<\\varepsilon<1 , \\] where $Z$ is a standard $n$-dimensional Gaussian vectors, $\\alpha_p>0$ is a constant depending only on $p$ and $C,c>0$ are absolute constants. As a con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07289","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"}