Affiliation:
1. Department of Mathematics, University of Washington, Box 354350, Seattle, Washington 98195, USA
Abstract
We study the global fluctuations for linear statistics of the form [Formula: see text] as n → ∞, for C1 functions f, and λ1, …, λn 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.
Publisher
World Scientific Pub Co Pte Lt
Subject
Discrete Mathematics and Combinatorics,Statistics, Probability and Uncertainty,Statistics and Probability,Algebra and Number Theory
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