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• W2951736730 abstract "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. 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." @default.
• W2951736730 created "2019-06-27" @default.
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• W2951736730 date "2012-03-27" @default.
• W2951736730 modified "2023-09-27" @default.
• W2951736730 title "Global Fluctuations for Linear Statistics of beta-Jacobi Ensembles" @default.
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