{"paper":{"title":"Geometry of random sections of isotropic convex bodies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Antonis Tsolomitis, Apostolos Giannopoulos, Labrini Hioni","submitted_at":"2016-01-10T19:07:55Z","abstract_excerpt":"Let $K$ be an isotropic symmetric convex body in ${\\mathbb R}^n$. We show that a subspace $F\\in G_{n,n-k}$ of codimension $k=\\gamma n$, where $\\gamma\\in (1/\\sqrt{n},1)$, satisfies $$K\\cap F\\subseteq \\frac{c}{\\gamma }\\sqrt{n}L_K (B_2^n\\cap F)$$ with probability greater than $1-\\exp (-\\sqrt{n})$. Using a different method we study the same question for the $L_q$-centroid bodies $Z_q(\\mu )$ of an isotropic log-concave probability measure $\\mu $ on ${\\mathbb R}^n$. For every $1\\leq q\\leq n$ and $\\gamma\\in (0,1)$ we show that a random subspace $F\\in G_{n,(1-\\gamma )n}$ satisfies $Z_q(\\mu )\\cap F\\sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02254","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"}