Tail sums of Wishart and GUE eigenvalues beyond the bulk edge

Iain M. Johnstone

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arXiv · 1704.06398

Tail sums of Wishart and GUE eigenvalues beyond the bulk edge

Iain M. Johnstone

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Abstract

Consider the classical Gaussian unitary ensemble of size $N$ and the real Wishart ensemble $W_N(n,I)$. In the limits as $N \to \infty$ and $N/n \to \gamma > 0$, the expected number of eigenvalues that exit the upper bulk edge is less than one, 0.031 and 0.170 respectively, the latter number being independent of $\gamma$. 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.

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Iain M. Johnstone. 2017-04-21. Tail sums of Wishart and GUE eigenvalues beyond the bulk edge. https://arxiv.org/abs/1704.06398

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