{"paper":{"title":"On the geometry of random polytopes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Shahar Mendelson","submitted_at":"2019-02-05T12:55:39Z","abstract_excerpt":"We present a simple proof to a fact recently established in [5]: let $\\xi$ be a symmetric random variable that has variance $1$, let $\\Gamma=(\\xi_{ij})$ be an $N \\times n$ random matrix whose entries are independent copies of $\\xi$, and set $X_1,...,X_N$ to be the rows of $\\Gamma$. Then under minimal assumptions on $\\xi$ and as long as $N \\geq c_1n$, $$ c_2 \\bigl(B_\\infty^n \\cap \\sqrt{\\log(eN/n)} B_2^n \\bigr) \\subset {\\rm absconv}(X_1,...,X_N) $$ with high probability."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.01664","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"}