{"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. 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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0145","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}