Poisson convergence of eigenvalues of circulant type matrices

被引：0
|
作者：
Arup Bose
Rajat Subhra Hazra
Koushik Saha
机构：
[1] Indian Statistical Institute,Statistics and Mathematics Unit
来源：
Extremes | 2011年 / 14卷
关键词：
Circulant matrix; -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; 60B20; 60G55; 60F99;
D O I：
暂无
中图分类号：
学科分类号：
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：27
相关论文
共 50 条
  • [1] Poisson convergence of eigenvalues of circulant type matrices
    Bose, Arup
    Hazra, Rajat Subhra
    Saha, Koushik
    EXTREMES, 2011, 14 (04) : 365 - 392
  • [2] Circulant decomposition of a matrix and the eigenvalues of Toeplitz type matrices
    Hariprasad, M.
    Venkatapathi, Murugesan
    APPLIED MATHEMATICS AND COMPUTATION, 2024, 468
  • [3] Poisson convergence for the largest eigenvalues of heavy tailed random matrices
    Auffinger, Antonio
    Ben Arous, Gerard
    Peche, Sandrine
    ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, 2009, 45 (03): : 589 - 610
  • [4] EIGENVALUES OF CIRCULANT MATRICES AND A CONJECTURE OF RYSER
    Euler, Reinhardt
    Gallardo, Luis H.
    Rahavandrainy, Olivier
    KRAGUJEVAC JOURNAL OF MATHEMATICS, 2021, 45 (05): : 751 - 759
  • [5] Weak convergence in circulant matrices
    Cureg, E
    Mukherjea, A
    JOURNAL OF THEORETICAL PROBABILITY, 2005, 18 (04) : 983 - 1007
  • [6] Weak Convergence in Circulant Matrices
    E. Cureg
    A. Mukherjea
    Journal of Theoretical Probability, 2005, 18 : 983 - 1007
  • [7] Universality in the fluctuation of eigenvalues of random circulant matrices
    Adhikari, Kartick
    Saha, Koushik
    STATISTICS & PROBABILITY LETTERS, 2018, 138 : 1 - 8
  • [8] Distribution of eigenvalues of real symmetric palindromic Toeplitz matrices and circulant matrices
    Massey, Adam
    Miller, Steven J.
    Sinsheimer, John
    JOURNAL OF THEORETICAL PROBABILITY, 2007, 20 (03) : 637 - 662
  • [9] Distribution of Eigenvalues of Real Symmetric Palindromic Toeplitz Matrices and Circulant Matrices
    Adam Massey
    Steven J. Miller
    John Sinsheimer
    Journal of Theoretical Probability, 2007, 20 : 637 - 662
  • [10] Eigenvalues of a special kind of symmetric block circulant matrices
    Ligong W.
    Xueliang L.
    Hoede C.
    Applied Mathematics-A Journal of Chinese Universities, 2004, 19 (1) : 17 - 26
12345