We derive concentration inequalities for functions of the empirical measure of eigenvalues for large, random, self adjoint matrices, with not necessarily Gaussian entries. The results presented apply in particular to non-Gaussian Wigner and Wishart matrices. We also provide concentration bounds for non commutative functionals of random matrices.
"Concentration of the Spectral Measure for Large Matrices." Electron. Commun. Probab. 5 119 - 136, 2000. https://doi.org/10.1214/ECP.v5-1026