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Statistics of spectral properties of matrix-valued random variables.

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Convergence of edge eigenvalues for Gaussian matrices

Let $\mu_{\mathsf{sc}}$ be the probability measuere of the semicircle law. For any $0<\varepsilon <2$, by Wigner's semicircle law, we have $$ \#\left\{\lambda_i \left(\frac{X}{\sqrt{n}}\right)\in[2-\v …
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