Asymptotic Spectra of Matrix-Valued Functions of Independent Random Matrices and Free Probability

Abstract

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.

some references added; some typos corrected

References in corpus (3)

• Central limit theorem for linear eigenvalue statistics of random matrices with independent entries
• On the Asymptotic Spectrum of Products of Independent Random Matrices
• On the asymptotic distribution of singular values of products of large rectangular random matrices

Cited by in corpus (1)

• Bulk and soft-edge universality for singular values of products of Ginibre random matrices