{"paper":{"title":"Smallest eigenvalue distributions for two classes of $\\beta$-Jacobi ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DC","cs.NA","math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Ioana Dumitriu","submitted_at":"2010-09-23T18:31:26Z","abstract_excerpt":"We compute the exact and limiting smallest eigenvalue distributions for two classes of $\\beta$-Jacobi ensembles not covered by previous studies. In the general $\\beta$ case, these distributions are given by multivariate hypergeometric ${}_2F_{1}^{2/\\beta}$ functions, whose behavior can be analyzed asymptotically for special values of $\\beta$ which include $\\beta \\in 2\\mathbb{N}_{+}$ as well as for $\\beta = 1$. Interest in these objects stems from their connections (in the $\\beta = 1,2$ cases) to principal submatrices of Haar-distributed (orthogonal, unitary) matrices appearing in randomized, c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4677","kind":"arxiv","version":2},"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"}