Eigenvalues of large chiral non-Hermitian random matrices

被引:2
|
作者
Chang, Shuhua [1 ]
Jiang, Tiefeng [2 ]
Qi, Yongcheng [3 ]
机构
[1] Tianjin Univ Finance & Econ, Coordinated Innovat Ctr Computable Modeling Manag, Tianjin 300222, Peoples R China
[2] Univ Minnesota, Sch Stat, 224 Church St SE, Minneapolis, MN 55455 USA
[3] Univ Minnesota, Dept Math & Stat, Duluth, MN 55812 USA
关键词
DISTRIBUTIONS; PRODUCTS;
D O I
10.1063/1.5088607
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We study a non-Hermitian chiral random matrix of which the eigenvalues are complex random variables. The empirical distributions and the radius of the eigenvalues are investigated. The limit of the empirical distributions is a new probability distribution defined on the complex plane. The graphs of the density functions are plotted; the surfaces formed by the density functions are understood through their convexity and their Gaussian curvatures. The limit of the radius is a Gumbel distribution. The main observation is that the joint density function of the eigenvalues of the chiral ensemble, after a transformation, becomes a rotation-invariant determinantal point process on the complex plane. Then, the eigenvalues are studied by the tools developed by Jiang and Qi [J. Theor. Probab. 30, 326 (2017); 32, 353 (2019)]. Most efforts are devoted to deriving the central limit theorems for distributions defined by the Bessel functions via the method of steepest descent and the estimates of the zero of a non-trivial equation as the saddle point.
引用
收藏
页数:31
相关论文
共 50 条
  • [1] Deviation probabilities for extremal eigenvalues of large Chiral non-Hermitian random matrices
    Ma, Yutao
    Wang, Siyu
    [J]. FORUM MATHEMATICUM, 2024,
  • [2] Resonances as eigenvalues of non-Hermitian Random Matrices
    Fyodorov, YV
    Sommers, HJ
    [J]. 5TH WIGNER SYMPOSIUM, PROCEEDINGS, 1998, : 287 - 289
  • [3] Wigner surmise for Hermitian and non-Hermitian chiral random matrices
    Akemann, G.
    Bittner, E.
    Phillips, M. J.
    Shifrin, L.
    [J]. PHYSICAL REVIEW E, 2009, 80 (06):
  • [4] COMPUTING COMPLEX EIGENVALUES OF LARGE NON-HERMITIAN MATRICES
    KERNER, W
    LERBINGER, K
    STEUERWALD, J
    [J]. COMPUTER PHYSICS COMMUNICATIONS, 1985, 38 (01) : 27 - 37
  • [5] Spectral Radii of Large Non-Hermitian Random Matrices
    Tiefeng Jiang
    Yongcheng Qi
    [J]. Journal of Theoretical Probability, 2017, 30 : 326 - 364
  • [6] Spectral Radii of Large Non-Hermitian Random Matrices
    Jiang, Tiefeng
    Qi, Yongcheng
    [J]. JOURNAL OF THEORETICAL PROBABILITY, 2017, 30 (01) : 326 - 364
  • [7] A Multilevel Spectral Indicator Method for Eigenvalues of Large Non-Hermitian Matrices
    Huang, Ruihao
    Sun, Jiguang
    Yang, Chao
    [J]. CSIAM TRANSACTIONS ON APPLIED MATHEMATICS, 2020, 1 (03): : 463 - 477
  • [8] REFINED PERTURBATION BOUNDS FOR EIGENVALUES OF HERMITIAN AND NON-HERMITIAN MATRICES
    Ipsen, I. C. F.
    Nadler, B.
    [J]. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 2009, 31 (01) : 40 - 53
  • [9] ON WORDS OF NON-HERMITIAN RANDOM MATRICES
    Dubach, Guillaume
    Peled, Yuval
    [J]. ANNALS OF PROBABILITY, 2021, 49 (04): : 1886 - 1916
  • [10] Eigenvalues of non-Hermitian random matrices and Brown measure of non-normal operators: Hermitian reduction and linearization method
    Belinschi, Serban T.
    Sniady, Piotr
    Speicher, Roland
    [J]. LINEAR ALGEBRA AND ITS APPLICATIONS, 2018, 537 : 48 - 83