Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices

doi:10.1007/s00362-016-0860-x

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	Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices
	Xia, Ningning 1; Bai, Zhidong 2,3
刊名	STATISTICAL PAPERS
	2019-06
卷号	60 期号:3 页码:633-665
关键词	Wigner matrices Eigenvectors Empirical spectral distribution Semicircular law Convergence rate
ISSN号	0932-5026
DOI	10.1007/s00362-016-0860-x
英文摘要	In this paper, we adopt the eigenvector empirical spectral distribution (VESD) to investigate the limiting behavior of eigenvectors of a large dimensional Wigner matrix Wn. In particular, we derive the optimal bound for the rate of convergence of the expected VESD of Wn to the semicircle law, which is of order O(n-1/2) under the assumption of having finite 10th moment. We further show that the convergence rates in probability and almost surely of the VESD are O(n-1/4) and O(n-1/6), respectively, under finite eighth moment condition. Numerical studies demonstrate that the convergence rate does not depend on the choice of unit vector involved in the VESD function, and the best possible bound for the rate of convergence of the VESD is of order O(n-1/2).
WOS研究方向	Mathematics
语种	英语
出版者	SPRINGER
WOS记录号	WOS:000467659900017
内容类型	期刊论文
源URL	[http://10.2.47.112/handle/2XS4QKH4/243]
专题	上海财经大学
通讯作者	Xia, Ningning
作者单位	1.Shanghai Univ Finance & Econ, Shanghai Key Lab Financial Informat Technol, Sch Stat & Management, 777 Guo Ding Rd, Shanghai 200433, Peoples R China; 2.Northeast Normal Univ, KLASMOE, 5268 Peoples Rd, Changchun 130024, Jilin, Peoples R China; 3.Northeast Normal Univ, Sch Math & Stat, 5268 Peoples Rd, Changchun 130024, Jilin, Peoples R China
推荐引用方式 GB/T 7714	Xia, Ningning,Bai, Zhidong. Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices[J]. STATISTICAL PAPERS,2019,60(3):633-665.
APA	Xia, Ningning,&Bai, Zhidong.(2019).Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices.STATISTICAL PAPERS,60(3),633-665.
MLA	Xia, Ningning,et al."Convergence rate of eigenvector empirical spectral distribution of large Wigner matrices".STATISTICAL PAPERS 60.3(2019):633-665.