{"paper":{"title":"Superconcentration, and randomized Dvoretzky's theorem for spaces with 1-unconditional bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.MG","authors_text":"Konstantin Tikhomirov","submitted_at":"2017-02-02T22:39:39Z","abstract_excerpt":"Let $n$ be a sufficiently large natural number and let $B$ be an origin-symmetric convex body in $R^n$ in the $\\ell$-position, and such that the normed space $(R^n,\\|\\cdot\\|_B)$ admits a $1$-unconditional basis. Then for any $\\varepsilon\\in(0,1/2]$, and for random $c\\varepsilon\\log n/\\log\\frac{1}{\\varepsilon}$-dimensional subspace $E$ distributed according to the rotation-invariant (Haar) measure, the section $B\\cap E$ is $(1+\\varepsilon)$-Euclidean with probability close to one. This shows that the \"worst-case\" dependence on $\\varepsilon$ in the randomized Dvoretzky theorem in the $\\ell$-posi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.00859","kind":"arxiv","version":3},"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"}