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

Electronic Communications in Probability

Yanhui Wang¹ 

关键词: order statistics;    moduli of eigenvalues;    polynomial ensembles;    products of random matrices;   

DOI  :  10.1214/18-ECP124

学科分类：统计和概率

来源: Institute of Mathematical Statistics

【 摘 要 】

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.

【 授权许可】

CC BY