We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C 1 functions f, and λ 1 , …, λ n being the eigenvalues of a (general) β-Jacobi ensemble. The fluctuation from the mean [Formula: see text] turns out to be given asymptotically by a Gaussian process. We compute the covariance matrix for the process and show that it is diagonalized by a shifted Chebyshev polynomial basis; in addition, we analyze the deviation from the predicted mean for polynomial test functions, and we obtain a law of large numbers.
No takes yet. Share an insight, caveat, or question.
Dumitriu et al. (2012) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: