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We investigate the asymptotic behavior of the maximal radius sequence induced by the sequence $(\\alpha_n)_{n \\geq1}$ defined for every $n \\geq1$ by $\\rho(\\alpha_n) = \\max{|a|, a \\in\\alpha_n}$. When $\\card(\\supp(P))$ is infinite, the maximal radius sequence goes to $\\sup{|x|, x \\in\\operatorname{supp}(P)}$ as $n$ goes to infinity. We then give the exact rate of convergence for two class"},"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":"0806.0918","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-06-05T07:40:13Z","cross_cats_sorted":[],"title_canon_sha256":"32bc2d86079a142fd01f5d67859d065cf79d028f1b0d26af3841082196a84fcb","abstract_canon_sha256":"79e6ca2360c43899773167430b0b0c235f0f2cef094d014e7300c7f45430dae9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:49.819508Z","signature_b64":"hfceJQpL5qi82WF5kroDUyhqo57cw6FkDhTh3OINpdeZgkCvyyqsZvmzU1EabAAdrxZTB9KFIF+FqtSIVS7ECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d033acbe4517eee8c136c158dc97d8fa13620d6695f38273d395b7c8ee76cd1d","last_reissued_at":"2026-05-18T03:59:49.819035Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:49.819035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of the maximal radius of an $L^r$-optimal sequence of quantizers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Abass Sagna (LPMA), Gilles Pag\\`es (LPMA)","submitted_at":"2008-06-05T07:40:13Z","abstract_excerpt":"Let $P$ be a probability distribution on $\\mathbb{R}^d$ (equipped with an Euclidean norm $|\\cdot|$). Let $ r> 0 $ and let $(\\alpha_n)_{n \\geq1}$ be an (asymptotically) $L^r(P)$-optimal sequence of $n$-quantizers. We investigate the asymptotic behavior of the maximal radius sequence induced by the sequence $(\\alpha_n)_{n \\geq1}$ defined for every $n \\geq1$ by $\\rho(\\alpha_n) = \\max{|a|, a \\in\\alpha_n}$. When $\\card(\\supp(P))$ is infinite, the maximal radius sequence goes to $\\sup{|x|, x \\in\\operatorname{supp}(P)}$ as $n$ goes to infinity. 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