Random Matrix Ensembles
Percy Deift, Guillaume Dubach, Carlos Tomei, Thomas Trogdon · Cambridge University Press eBooks · 2025
We now introduce the results from random matrix theory that are needed to prove Theorem 6.2 and Proposition 6.5 in the next chapter.Let H be an N x N Hermitian (or real symmetric) matrix with eigenvalues λ1≥λ2≥⋯≥λN and let β1,β2,…,βN denote the absolute value of the first components of the normalized eigenvectors.We assume the entries of H are distributed according to an invariant or generalized Wigner ensemble (see Section 5.1).