A relatively obscure eigenvalue due to Wielandt is used to give a simple derivation of the asymptotic distribution of the eigenvalues of a random symmetric matrix. The asymptotic distributions are obtained under a fairly general setting. An application of the general theory to the bootstrap distribution of the eigenvalues of the sample covariance matrix is given.
"On Wielandt's Inequality and Its Application to the Asymptotic Distribution of the Eigenvalues of a Random Symmetric Matrix." Ann. Statist. 19 (1) 260 - 271, March, 1991. https://doi.org/10.1214/aos/1176347980