FLUCTUATIONS OF LINEAR EIGENVALUE STATISTICS OF RANDOM BAND MATRICES

被引：14
|
作者：
Jana, I. [1 ]
Saha, K. [2 ]
Soshnikov, A. [1 ]
机构：
[1] Univ Calif Davis, Dept Math, Davis, CA 95616 USA
[2] Indian Inst Technol, Dept Math, Bombay, Maharashtra, India
来源：
THEORY OF PROBABILITY AND ITS APPLICATIONS | 2016年 / 60卷 / 03期
关键词：
band random matrix; central limit theorem; Gaussian distribution; linear eigenvalue statistics; semicircular law; Wigner matrix; CENTRAL-LIMIT-THEOREM; CHARACTERISTIC VECTORS; SCALING PROPERTIES; BORDERED MATRICES; WIGNER;
D O I：
10.1137/S0040585X97T987788
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
In this paper, we study the fluctuation of linear eigenvalue statistics of random band matrices defined by M-n = 1/root b(n) W-n, where W-n is an n x n band Hermitian random matrix of bandwidth b(n); i.e., the diagonal elements and only the first b(n) off-diagonal elements are nonzero. We study the linear eigenvalue statistics N(phi) - Sigma(n)(i=1) phi(lambda(i)) of such matrices, where lambda(i) are the eigenvalues of M-n and phi is a sufficiently smooth function. We prove that root b(n)/n [N(phi) - EN(phi)] ->(d) N(0, V(phi)) for b(n) >> root n, where V (phi) is given in Theorem 1.
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页码：407 / 443
页数：37
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