This paper investigates the strong limiting behavior of the eigenvalues of the class of matrices $\frac{1}{N}(D_n\circ X_n){(D_n\circ X_n)}^{\ast }$, studied in [V. L. Girko, Theory of Stochastic Canonical Equations: Vol. $1$ (Kluwer Academic Publishers, Dordrecht, 2001)]. Here, $X_n=(x_{ij})$ is an $n\times N$ random matrix consisting of independent complex standardized random variables, $D_n=(d_{ij})$, $n\times N$, has nonnegative entries, and ∘ denotes Hadamard (componentwise) product. Results are obtained under assumptions on the entries of $X_n$ and $D_n$ which are different from those in [V. L. Girko, Theory of Stochastic Canonical Equations: Vol. 1 (Kluwer Academic Publishers, Dordrecht, 2001)], which include a Lindeberg condition on the entries of $D_n\circ X_n$, as well as a bound on the average of the rows and columns of $D_n\circ D_n$. The present paper separates the assumptions needed on $X_n$ and $D_n$. It assumes a Lindeberg condition on the entries of $X_n$, along with a tightness-like condition on the entries of $D_n$.

本文研究了矩阵类的特征值的强限制行为$\frac{\mathrm{1个}}{否}({丁}_n\circ X_n){({丁}_n\circ X_n)}^{＊}$, 研究于 [V. L. Girko，随机正则方程理论：卷。 $\mathrm{1个}$(Kluwer Academic Publishers, Dordrecht, 2001)]。这里，$X_n=(X_{我j})$是一个$n\times 否$由独立的复杂标准化随机变量组成的随机矩阵，${丁}_n=(d_{我j})$,$n\times 否$, 具有非负项，并且 ∘ 表示 Hadamard（分量）产品。结果是在对条目的假设下获得的$X_n$和${丁}_n$这与 [V. L. Girko，随机正则方程理论：卷。1 (Kluwer Academic Publishers, Dordrecht, 2001)]，其中包括关于条目的 Lindeberg 条件${丁}_n\circ X_n$，以及行和列的平均值的界限${丁}_n\circ {丁}_n$. 本文将所需的假设分开$X_n$和${丁}_n$. 它假设条目的 Lindeberg 条件$X_n$，以及条目上的类似紧度的条件${丁}_n$.