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.
Citation
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
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