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Distribution of Linear Statistics of Singular Values of the Product of Random Matrices by Götze, Friedrich; Naumov, Alexey; Tikhomirov, Alexander is a scholarly article available to read on EtoBox.

What is Distribution of Linear Statistics of Singular Values of the Product of Random Matrices about?

In this paper we consider the product of two independent random matrices $\mathbb X^{(1)}$ and $\mathbb X^{(2)}$. Assume that $X_{jk}^{(q)}, 1 \le j,k \le n, q = 1, 2,$ are i.i.d. random variables with $\mathbb E X_{jk}^{(q)} = 0, \mathbb E (X_{jk}^{(q)})^2 = 1$. Denote by $s_1, ..., s_n$ the singular values of $\mathbb W: = \frac{1}{n} \mathbb X^{(1)} \mathbb X^{(2)}$. We prove the central limit theorem for linear statistics of the squared singular values $s_1^2, ..., s_n^2$ showing that the limiting variance depends on $\kappa_4: = \mathbb E (X_{11}^{1})^4 - 3$.

Author

Götze, Friedrich; Naumov, Alexey; Tikhomirov, Alexander

Published

2014

Language

EN