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Silverstein, Jamal Najim, Malika Kharouf, Walid Hachem","submitted_at":"2011-07-01T08:36:05Z","abstract_excerpt":"In this article, we study the fluctuations of the random variable: $$ {\\mathcal I}_n(\\rho) = \\frac 1N \\log\\det(\\Sigma_n \\Sigma_n^* + \\rho I_N),\\quad (\\rho>0) $$ where $\\Sigma_n= n^{-1/2} D_n^{1/2} X_n\\tilde D_n^{1/2} +A_n$, as the dimensions of the matrices go to infinity at the same pace. Matrices $X_n$ and $A_n$ are respectively random and deterministic $N\\times n$ matrices; matrices $D_n$ and $\\tilde D_n$ are deterministic and diagonal, with respective dimensions $N\\times N$ and $n\\times n$; matrix $X_n=(X_{ij})$ has centered, independent and identically distributed entries with unit varian"},"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":"1107.0145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-07-01T08:36:05Z","cross_cats_sorted":["math.ST","stat.TH"],"title_canon_sha256":"625eeab1035572e6902dce73b22b941768b4f090874b75ea3ea97263e5a891d2","abstract_canon_sha256":"c484efc3c241e7336b7d656c509956c9c0982f387a200b0f0ddfb079c1a2497a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:19:02.586566Z","signature_b64":"D4E6h7jD6ALmWVgz2lJOm0KjTMTOv9ncOKldj8lCQkyXkTXVxT5UI76bRoCUdzH+x+LcxyICNca1VySE8hv9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"42e2f6ba1ee67aa0b0076b30a8832bf045bdda1dc2810be7c4b0d33db0302fef","last_reissued_at":"2026-05-18T04:19:02.585975Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:19:02.585975Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A CLT for Information-theoretic statistics of Non-centered Gram random matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Jack W. 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