Global Fluctuations for Linear Statistics of \beta-Jacobi Ensembles
RANDOM MATRICES-THEORY AND APPLICATIONS(2012)
摘要
We study the global fluctuations for linear statistics of the form Sigma(n)(i=1) f (lambda(i)) as n -> infinity, for C-1 functions f, and lambda(1),...,lambda(n) being the eigenvalues of a (general) beta-Jacobi ensemble. The fluctuation from the mean (Sigma(n)(i=1) f (lambda(i)) - E Sigma(n)(i=1) f (lambda(i))) 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.
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关键词
Random matrices,eigenvalues,Jacobi ensemble,linear statistics
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