Asymptotic spectra of matrix-valued functions of independent random matrices and free probability

Götze F, Kösters H, Tikhomirov A. Asymptotic spectra of matrix-valued functions of independent random matrices and free probability. RANDOM MATRICES-THEORY AND APPLICATIONS. 2015;4(2): 85.We investigate the universality of singular value and eigenvalue distributions of matrix-valued functions of independent random matrices and apply these general results in several examples. In particular we determine the limit distribution and prove universality under general conditions for singular value and eigenvalue distributions of products of independent matrices from spherical ensembles