{"paper":{"title":"Exact Statistical Characterization of $2\\times2$ Gram Matrices with Arbitrary Variance Profile","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT","math.PR"],"primary_cat":"cs.IT","authors_text":"David Morales-Jimenez, Matthew McKay, Nicolas Auguin","submitted_at":"2017-04-12T05:48:59Z","abstract_excerpt":"This paper is concerned with the statistical properties of the Gram matrix $\\mathbf{W}=\\mathbf{H}\\mathbf{H}^\\dagger$, where $\\mathbf{H}$ is a $2\\times2$ complex central Gaussian matrix whose elements have arbitrary variances. With such arbitrary variance profile, this random matrix model fundamentally departs from classical Wishart models and presents a significant challenge as the classical analytical toolbox no longer directly applies. We derive new exact expressions for the distribution of $\\mathbf{W}$ and that of its eigenvalues by means of an explicit parameterization of the group of unit"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05214","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"}