A Quantitative Central Limit Theorem for Linear Statistics of Random Matrix Eigenvalues

被引：0
作者：
Christian Döbler
Michael Stolz
机构：
[1] Ruhr-Universität Bochum,Fakultät für Mathematik
来源：
Journal of Theoretical Probability | 2014年 / 27卷
关键词：
Random matrices; Haar measure; Unitary group; Speed of convergence; Central limit theorem; Traces of powers; 60F05; 60B15; 60B20;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost 1/n can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein’s method of exchangeable pairs.
引用
收藏
页码：945 / 953
页数：8
相关论文
共 12 条
[1]  
Chatterjee S.(2009)Fluctuations of eigenvalues and second order Poincaré inequalities Probab. Theory Relat. Fields 143 1-40
[2]  
Costin O.(1995)Gaussian fluctuation in random matrices Phys. Rev. Lett. 75 69-72
[3]  
Lebowitz J.L.(2001)Linear functionals of eigenvalues of random matrices Trans. Am. Math. Soc. 353 2615-2633
[4]  
Diaconis P.(2011)Stein’s method and the multivariate CLT for traces of powers on the classical compact groups Electron. J. Probab. 16 2375-2405
[5]  
Evans S.N.(2012)Stein’s method, heat kernel, and traces of powers of elements of compact Lie groups Electron. J. Probab. 17 1-16
[6]  
Döbler C.(1997)On random matrices from the compact classical groups Ann. Math. (2) 145 519-545
[7]  
Stolz M.(2000)The central limit theorem for local linear statistics in classical compact groups and related combinatorial identities Ann. Probab. 28 1353-1370
[8]  
Fulman J.(2005)On the Diaconis–Shahshahani method in random matrix theory J. Algebr. Comb. 22 471-491
[9]  
Johansson K.(2002)Eigenvalue distributions of random unitary matrices Probab. Theory Relat. Fields 123 202-224
[10]  
Soshnikov A.(undefined)undefined undefined undefined undefined-undefined
12