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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."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1902.01664","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-02-05T12:55:39Z","cross_cats_sorted":[],"title_canon_sha256":"47a36223995a01890ae7d53d5313034c0388e366d569757168c344d2c9754f98","abstract_canon_sha256":"627b4ff9dbcbce26e2b7df0e74c85e9862a9c6082ee39c2f1d961f0f829193d2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:47.032695Z","signature_b64":"yajPJYMe3ROCveLKQjpVYKXLXJHpqhZ8HbtD9CnOgIO3sFTBXkNS/p7uJFJ8fW1OMQTpJMjqD0F3bRalTpHyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3b4954ab74d614f2e469bfd230906c82e8e1ab9e32a4b2a5f86caf23e5a68598","last_reissued_at":"2026-05-17T23:54:47.032193Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:47.032193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\Gamma$. 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