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Statistics of spectral properties of matrix-valued random variables.
2
votes
1
answer
118
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Functional calculation for Hermitian matrices
First, let me recall some useful definitions
We recall that if $A=U \Lambda U^*$ is a Hermitian matrix with $U U^*=U^* U=I$ and $\Lambda=\operatorname{diag}\left(\lambda_1\right)$ and $f: \mathbb{R} \ …
0
votes
1
answer
57
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Convergence of edge eigenvalues for Gaussian matrices
I am reading this lecture note.
I have a difficulty in understanding the third section in chapter 6. Particularly, in Theorem 4.1, they claimed that
Let $X$ be a Gaussian Wigner matrix satisfying ass …