Electronic Communications in Probability

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

Yanhui Wang

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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

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

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

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Zentralblatt MATH identifier

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

order statistics moduli of eigenvalues polynomial ensembles products of random matrices

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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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