## Electronic Communications in Probability

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

Yanhui Wang

#### 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
Accepted: 5 March 2018
First available in Project Euclid: 30 March 2018

https://projecteuclid.org/euclid.ecp/1522375377

Digital Object Identifier
doi:10.1214/18-ECP124

Mathematical Reviews number (MathSciNet)
MR3785395

Zentralblatt MATH identifier
1390.60041

#### 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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