Electronic Communications in Probability

Order statistics of the moduli of the eigenvalues of product random matrices from polynomial ensembles

Yanhui Wang

Full-text: Open access

Abstract

Let $X_{1}, \ldots , X_{m_{N}}$ be independent random matrices of order $N$ drawn from the polynomial ensembles of derivative type. For any fixed $n$, we consider the limiting distribution of the $n$th largest modulus of the eigenvalues of $X = \prod _{k=1}^{m_{N}}X_{k}$ as $N \to \infty $ where $m_{N}/N$ converges to some constant $\tau \in [0, \infty )$. In particular, we find that the limiting distributions of spectral radii behave like that of products of independent complex Ginibre matrices.

Article information

Source
Electron. Commun. Probab., Volume 23 (2018), paper no. 21, 14 pp.

Dates
Received: 5 July 2017
Accepted: 5 March 2018
First available in Project Euclid: 30 March 2018

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1522375377

Digital Object Identifier
doi:10.1214/18-ECP124

Mathematical Reviews number (MathSciNet)
MR3785395

Zentralblatt MATH identifier
1390.60041

Subjects
Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see 15B52) 41A60: Asymptotic approximations, asymptotic expansions (steepest descent, etc.) [See also 30E15]

Keywords
order statistics moduli of eigenvalues polynomial ensembles products of random matrices

Rights
Creative Commons Attribution 4.0 International License.

Citation

Wang, Yanhui. Order statistics of the moduli of the eigenvalues of product random matrices from polynomial ensembles. Electron. Commun. Probab. 23 (2018), paper no. 21, 14 pp. doi:10.1214/18-ECP124. https://projecteuclid.org/euclid.ecp/1522375377


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