Global Fluctuations for Linear Statistics of Β-jacobi Ensembles
نویسنده
چکیده
We study the global fluctuations for linear statistics of the form ∑ n i=1 f(λi) as n → ∞, for C functions f , and λ1, . . . , λn being the eigenvalues of a (general) β-Jacobi ensemble [18, 29]. The fluctuation from the mean ( ∑ n i=1 f(λi)− E ∑ n i=1 f(λi)) is 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.
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تاریخ انتشار 2012