GLOBAL FLUCTUATIONS FOR LINEAR STATISTICS OF β-JACOBI ENSEMBLES

被引：34

作者：

Dumitriu, Ioana ^{[1
]}

Paquette, Elliot ^{[1
]}

机构：

[1] Univ Washington, Dept Math, Box 354350, Seattle, WA 98195 USA

来源：

RANDOM MATRICES-THEORY AND APPLICATIONS | 2012年 / 1卷 / 04期

关键词：

Random matrices; eigenvalues; Jacobi ensemble; linear statistics; CENTRAL-LIMIT-THEOREM; RANDOM MATRICES; EIGENVALUES; DISTRIBUTIONS; UNIVERSALITY; PRODUCT; CLT;

D O I：

10.1142/S201032631250013X

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

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.

引用

页数：60