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