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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.6103","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-03-27T23:02:02Z","cross_cats_sorted":[],"title_canon_sha256":"6dc000bf0fbd6c99736b12774cec10df989bfad371bc37f63145286880432208","abstract_canon_sha256":"13f2e5f751357e9addeb4e260f00eac85ec00408d62de81e98a3bd2610103544"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:44:13.558733Z","signature_b64":"4TMDOK1O3x81OUhqsjUrMVxGCDcF6TClLcHpatFK7SJkD/KCQOI0RTgYW7vLaJRZ2tJgZwIo7R/C7Ie+0bqKBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9155a82e69989302e07a53cbc7777a368d2525662769825a1409aa682721a053","last_reissued_at":"2026-05-18T03:44:13.558332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:44:13.558332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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