For linear spectral statistics of Wigner matrix, we establish a CLT when the entries are independent, standardised with however inhomogeneous fourth moments. Formulas for the expectation and the variance of the Gaussian limiting distribution are given. An application to the normalized stochastic block model is further proposed.

中文翻译：

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关于具有不齐四阶矩的 Wigner 矩阵的线性特征值统计的 CLT 的推广

对于 Wigner 矩阵的线性谱统计，我们在条目独立时建立一个 CLT，标准化但不均匀的四阶矩。给出了高斯极限分布的期望和方差的公式。进一步提出了对归一化随机块模型的应用。