{"paper":{"title":"Global Fluctuations for Linear Statistics of \\beta-Jacobi Ensembles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Elliot Paquette, Ioana Dumitriu","submitted_at":"2012-03-27T23:02:02Z","abstract_excerpt":"We study the global fluctuations for linear statistics of the form $\\sum_{i=1}^n f(\\lambda_i)$ as $n \\rightarrow \\infty$, for $C^1$ functions $f$, and $\\lambda_1, ..., \\lambda_n$ being the eigenvalues of a (general) $\\beta$-Jacobi ensemble, for which tridiagonal models were given by Killip and Nenciu as well as Edelman and Sutton. The fluctuation from the mean ($\\sum_{i=1}^n f(\\lambda_i) - \\Exp \\sum_{i=1}^n f(\\lambda_i)$) is given asymptotically by a Gaussian process.\n  We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.6103","kind":"arxiv","version":3},"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"}