{"paper":{"title":"Extreme Eigenvalue Distributions of Some Complex Correlated Non-Central Wishart and Gamma-Wishart Random Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","stat.TH"],"primary_cat":"math.ST","authors_text":"Matthew R. McKay, Prathapasinghe Dharmawansa","submitted_at":"2011-01-05T15:12:45Z","abstract_excerpt":"Let $\\mathbf{W}$ be a correlated complex non-central Wishart matrix defined through $\\mathbf{W}=\\mathbf{X}^H\\mathbf{X}$, where $\\mathbf{X}$ is $n\\times m \\, (n\\geq m)$ complex Gaussian with non-zero mean $\\boldsymbol{\\Upsilon}$ and non-trivial covariance $\\boldsymbol{\\Sigma}$. We derive exact expressions for the cumulative distribution functions (c.d.f.s) of the extreme eigenvalues (i.e., maximum and minimum) of $\\mathbf{W}$ for some particular cases. These results are quite simple, involving rapidly converging infinite series, and apply for the practically important case where $\\boldsymbol{\\U"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.1001","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"}