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The strong circular law theorem states that with probability one, the empirical spectral distribution $\\frac{1}{n}(\\de_{\\la_{n,1}}+...+\\de_{\\la_{n,n}})$ converges weakly as $n\\to\\infty$ to the uniform law over the unit disc $\\{z\\in\\dC;|z|\\leq1\\}$. In this short note, we provide an elementary argument that allows to add a deterministic matrix $M$ to $(X_{jk})_{1\\leq j,k\\leq n}$ provided"},"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":"0709.0036","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2007-09-01T06:57:30Z","cross_cats_sorted":[],"title_canon_sha256":"3887d9044b47fc8bf8183a7f9b4e714549ea1476e7bcb2faba9e50995def9d5c","abstract_canon_sha256":"0538c66bb3a4bc7631623a4082657fd09983f1d2e020f4bd679dc37e1ac7db16"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:36:51.546302Z","signature_b64":"uWZEfgdAwxTWR7SWRnOJYVZRcRPpEsjFCpTL26S8mslNfhGDYf1YELaNbkAKu4Igz8QgwOWcuNep6LFx++J2Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8ff6d83a0e67a5949b03f406f8f0533aca7105678d02c7c5e431c9f107138a65","last_reissued_at":"2026-05-18T04:36:51.545740Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:36:51.545740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Circular law for non-central random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Djalil Chafai (LAMA)","submitted_at":"2007-09-01T06:57:30Z","abstract_excerpt":"Let $(X_{jk})_{j,k\\geq 1}$ be an infinite array of i.i.d. complex random variables, with mean 0 and variance 1. 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