We consider large-dimensional Hermitian or symmetric random matrices of the form [Formula: see text], where [Formula: see text] is a Wigner matrix and [Formula: see text] is a real diagonal matrix whose entries are independent of [Formula: see text]. For a large class of diagonal matrices [Formula: see text], we prove that the fluctuations of linear spectral statistics of [Formula: see text] for [Formula: see text] test function can be decomposed into that of [Formula: see text] and of [Formula: see text], and that each of those weakly converges to a Gaussian distribution. We also calculate the formulae for the means and variances of the limiting distributions.

中文翻译：

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变形 Wigner 矩阵线性谱统计的高斯涨落

我们考虑 [Formula: see text] 形式的大维 Hermitian 或对称随机矩阵，其中 [Formula: see text] 是 Wigner 矩阵， [Formula: see text] 是一个实对角矩阵，其条目独立于 [Formula : 见正文]。对于一大类对角矩阵[公式：见文]，我们证明[公式：见文]测试函数的[公式：见文]的线性谱统计波动可以分解为[公式：见文]的波动] 和 [公式：见正文]，并且这些中的每一个都弱收敛到高斯分布。我们还计算了极限分布的均值和方差的公式。