Joint convergence of several copies of different patterned random matrices

Abstract

We study the joint convergence of independent copies of several patterned matrices in the noncommutative probability setup. In particular, joint convergence holds for the well known Wigner, Toeplitz, Hankel, reverse circulant and symmetric circulant matrices. We also study some properties of the limits. In particular, we show that copies of Wigner becomes asymptotically free with copies of any of the above other matrices.

31 pages, 4 figures. Substantial change in the introduction. Typos corrected

References in corpus (3)

• The largest eigenvalue of rank one deformation of large Wigner matrices
• The largest eigenvalues of finite rank deformation of large Wigner matrices: convergence and nonuniversality of the fluctuations
• Asymptotics of unitary and othogonal matrix integrals