Poisson convergence of eigenvalues of circulant type matrices

被引：10
|
作者：
Bose, Arup [1 ]
Hazra, Rajat Subhra [1 ]
Saha, Koushik [1 ]
机构：
[1] Indian Stat Inst, Stat & Math Unit, Kolkata 700108, India
来源：
EXTREMES | 2011年 / 14卷 / 04期
关键词：
Circulant matrix; k-circulant matrix; Eigenvalues; Large dimensional random matrix; Moving average process; Normal approximation; Point process; Poisson random measure; Reverse circulant matrix; Spectral density; Symmetric circulant matrix; STATISTICS;
D O I：
10.1007/s10687-010-0115-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We consider the point processes based on the eigenvalues of the reverse circulant, symmetric circulant and k-circulant matrices with i.i.d. entries and show that they converge to a Poisson random measures in vague topology. The joint convergence of upper ordered eigenvalues and their spacings follow from this. We extend these results partially to the situation where the entries are come from a two sided moving average process.
引用
收藏
页码：365 / 392
页数：28
相关论文
共 50 条
  • [41] INVERTING CIRCULANT MATRICES
    SEARLE, SR
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1979, 25 (01) : 77 - 89
  • [42] ON THE INVERSION OF CIRCULANT MATRICES
    GOOD, IJ
    BIOMETRIKA, 1950, 37 (1-2) : 185 - 186
  • [43] On the logarithms of circulant matrices
    Lu, Chengbo
    JOURNAL OF COMPUTATIONAL ANALYSIS AND APPLICATIONS, 2013, 15 (03) : 402 - 412
  • [44] Random Circulant Matrices
    Merikoski, Jorma K.
    INTERNATIONAL STATISTICAL REVIEW, 2020, 88 (01) : 252 - 254
  • [45] Idempotent circulant matrices
    Radhakrishnan, M.
    Elumalai, N.
    Perumal, R.
    Arulprakasam, R.
    PROCEEDINGS OF THE 10TH NATIONAL CONFERENCE ON MATHEMATICAL TECHNIQUES AND ITS APPLICATIONS (NCMTA 18), 2018, 1000
  • [46] ON CIRCULANT BOOLEAN MATRICES
    DAODE, H
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1990, 136 : 107 - 117
  • [47] Circulant Type Matrices with the Sum and Product of Fibonacci and Lucas Numbers
    Jiang, Zhaolin
    Gong, Yanpeng
    Gao, Yun
    ABSTRACT AND APPLIED ANALYSIS, 2014,
  • [48] Double circulant matrices
    Fan, Yun
    Liu, Hualu
    LINEAR & MULTILINEAR ALGEBRA, 2018, 66 (10): : 2119 - 2137
  • [49] Some strong convergence theorems for eigenvalues of general sample covariance matrices
    Yin, Yanqing
    RANDOM MATRICES-THEORY AND APPLICATIONS, 2022, 11 (03)
  • [50] Poisson statistics for eigenvalues: From random Schrodinger operators to random CMV matrices
    Stoiciu, Mihai
    Probability and Mathematical Physics: A Volume in Honor of Stanislav Molchanov, 2007, 42 : 465 - 475
12345