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2018 Order statistics of the moduli of the eigenvalues of product random matrices from polynomial ensembles
Yanhui Wang
Electron. Commun. Probab. 23: 1-14 (2018). DOI: 10.1214/18-ECP124

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.

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Yanhui Wang. "Order statistics of the moduli of the eigenvalues of product random matrices from polynomial ensembles." Electron. Commun. Probab. 23 1 - 14, 2018. https://doi.org/10.1214/18-ECP124

Information

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

zbMATH: 1390.60041
MathSciNet: MR3785395
Digital Object Identifier: 10.1214/18-ECP124

Subjects:
Primary: 41A60, 60B20

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