Fluctuations of Linear Eigenvalues Statistics for Wigner Matrices: Edge Case

被引：1

作者：

Pan, Guangming ^{[1
]}

Wang, Shaochen ^{[2
]}

Zhou, Wang ^{[3
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

[2] South China Univ Technol, Sch Math, Guangzhou 510640, Guangdong, Peoples R China

[3] Natl Univ Singapore, Dept Stat & Appl Probabil, Singapore 117546, Singapore

来源：

JOURNAL OF STATISTICAL PHYSICS | 2016年 / 165卷 / 03期

基金：

中国博士后科学基金;

关键词：

Wigner matrix; Linear eigenvalue statistic; Fluctuation theorem; CENTRAL-LIMIT-THEOREM; UNIVERSALITY;

D O I：

10.1007/s10955-016-1618-5

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this note, we consider the fluctuation theorem for , where are eigenvalues from a Wigner matrix and . We prove that in the edge case behaves like the counting function of Wigner matrix. Our results can be viewed as a complement of Bao et al. (J Stat Phys 150(1):88-129, 2013).

引用

页码：507 / 520

页数：14

共 50 条

[21] Truncated Linear Statistics Associated with the Top Eigenvalues of Random Matrices
Grabsch, Aurelien
Majumdar, Satya N.
Texier, Christophe
JOURNAL OF STATISTICAL PHYSICS, 2017, 167 (02) : 234 - 259
[22] FLUCTUATIONS OF LINEAR EIGENVALUE STATISTICS OF RANDOM BAND MATRICES
Jana, I.
Saha, K.
Soshnikov, A.
THEORY OF PROBABILITY AND ITS APPLICATIONS, 2016, 60 (03) : 407 - 443
[23] Fluctuations of functions of Wigner matrices
Erdos, Laszlo
Schroder, Dominik
ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2016, 21
[24] RANDOM COVARIANCE MATRICES: UNIVERSALITY OF LOCAL STATISTICS OF EIGENVALUES UP TO THE EDGE
Wang, Ke
RANDOM MATRICES-THEORY AND APPLICATIONS, 2012, 1 (01)
[25] Universality of the edge distribution of eigenvalues of wigner random matrices with polynomially decaying distributions of entries
Ruzmaikina, A
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2006, 261 (02) : 277 - 296
[26] Universality of the Edge Distribution of Eigenvalues of Wigner Random Matrices with Polynomially Decaying Distributions of Entries
A. Ruzmaikina
Communications in Mathematical Physics, 2006, 261 : 277 - 296
[27] Central Limit Theorem for Partial Linear Eigenvalue Statistics of Wigner Matrices
Bao, Zhigang
Pan, Guangming
Zhou, Wang
JOURNAL OF STATISTICAL PHYSICS, 2013, 150 (01) : 88 - 129
[28] Gaussian fluctuation for linear eigenvalue statistics of large dilute Wigner matrices
Xie JunShan
SCIENCE CHINA-MATHEMATICS, 2014, 57 (06) : 1221 - 1236
[29] Central Limit Theorem for Partial Linear Eigenvalue Statistics of Wigner Matrices
Zhigang Bao
Guangming Pan
Wang Zhou
Journal of Statistical Physics, 2013, 150 : 88 - 129
[30] Partial Linear Eigenvalue Statistics for Wigner and Sample Covariance Random Matrices
O'Rourke, Sean
Soshnikov, Alexander
JOURNAL OF THEORETICAL PROBABILITY, 2015, 28 (02) : 726 - 744

← 1 2 3 4 5 →