We characterize the limiting fluctuations of traces of several independent Wigner matrices and deterministic matrices under mild conditions. A CLT holds but in general the families are not asymptotically free of second-order and the limiting covariance depends the limiting ∗-distribution of the deterministic matrices and their transposes and Hadamard products.

中文翻译：

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复杂 Wigner 和确定性矩阵的联合全局波动

我们描述了在温和条件下几个独立 Wigner 矩阵和确定性矩阵的迹线的极限波动。CLT 成立，但一般来说，这些族不是渐近无二阶的，并且限制协方差取决于限制*-确定性矩阵及其转置和Hadamard产品的分布。