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This is achieved using stochastic geometric techniques. Precisely, if $K$ is in isotropic position, we present a method to find centered simplices verifying the above bound that works with very high probability.\n  As a consequence, we provide correct asymptotic estimates on an old problem in convex geometry. Namely, we show that "},"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":"1707.03246","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2017-07-11T12:38:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"4b669cece1438273816aede73cf51ce2809cd81de7eb72399e13a72097f12fd5","abstract_canon_sha256":"57a6408c36d3a7a4508a1f97c817cb8c62262c8b31ca266c4b8d5e5eece80804"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:40:26.888811Z","signature_b64":"9l+m33GOPz889BdvGgMzRlzEV94FBAxUKy/p8Ae9hEv2O3j4K9Pcgy/rdsPhBROKaJYYTF7pRZQr9l1/AsFKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cd3757c5e75d4f13cca2c55ed83f40f832bedf47bcdb685cd6483b2e8a28497c","last_reissued_at":"2026-05-17T23:40:26.887780Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:40:26.887780Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The minimal volume of simplices containing a convex body","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.MG","authors_text":"Dami\\'an Pinasco, Daniel Galicer, Mariano Merzbacher","submitted_at":"2017-07-11T12:38:47Z","abstract_excerpt":"Let $K \\subset \\mathbb R^n$ be a convex body with barycenter at the origin. We show there is a simplex $S \\subset K$ having also barycenter at the origin such that $\\left(\\frac{vol(S)}{vol(K)}\\right)^{1/n} \\geq \\frac{c}{\\sqrt{n}},$ where $c>0$ is an absolute constant. This is achieved using stochastic geometric techniques. Precisely, if $K$ is in isotropic position, we present a method to find centered simplices verifying the above bound that works with very high probability.\n  As a consequence, we provide correct asymptotic estimates on an old problem in convex geometry. 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