Consider the classical Gaussian unitary ensemble of size N and the real white Wishart ensemble with N variables and n degrees of freedom. In the limits of large N and n, with positive ratio γ in the Wishart case, the expected number of eigenvalues that exit the upper bulk edge is less than one, approaching 0.031 and 0.170 respectively, the latter number being independent of γ. These statements are consequences of quantitative bounds on tail sums of eigenvalues outside the bulk which are established here for applications in high dimensional covariance matrix estimation.

中文翻译：

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超出体边缘的 Wishart 和高斯特征值的尾部和

考虑大小为 N 的经典高斯酉系综和具有 N 个变量和 n 个自由度的实白威沙特系综。在大 N 和 n 的限制下，在 Wishart 情况下，比率 γ 为正值时，离开上体边缘的特征值的预期数量小于 1，分别接近 0.031 和 0.170，后者的数量与 γ 无关。这些陈述是主体外部特征值尾部和的定量界限的结果，这些界限是为高维协方差矩阵估计中的应用而建立的。