Determinantal point processes in the plane from products of random matrices

被引：30

作者：

Adhikari, Kartick ^{[1
]}

Reddy, Nanda Kishore ^{[1
]}

Reddy, Tulasi Ram ^{[1
]}

Saha, Koushik ^{[2
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Indian Inst Technol, Dept Math, Bombay 400076, Maharashtra, India

来源：

ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES | 2016年 / 52卷 / 01期

关键词：

Determinantal point process; Eigenvalues; Empirical spectral distribution; Limiting spectral distribution; Haar measure; QR decomposition; Random matrix; RQ decomposition; Generalized Schur decomposition; Unitary matrix; Wedge product;

D O I：

10.1214/14-AIHP632

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

引用

页码：16 / 46

页数：31

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