{"paper":{"title":"Neighborhoods on the Grasmannian of marginals with bounded isotropic constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Grigoris Paouris, Petros Valettas","submitted_at":"2014-04-19T21:28:42Z","abstract_excerpt":"We show that for any isotropic log-concave probability measure $\\mu$ on $\\mathbb R^n$, for every $\\varepsilon > 0$, every $1 \\leq k \\leq \\sqrt{n}$ and any $E \\in G_{n,k}$ there exists $F \\in G_{n,k}$ with $d(E,F) < \\varepsilon$ and $L_{\\pi_F\\mu} < C/\\varepsilon$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4988","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"}