We study the joint convergence of independent copies of several patterned matrices in the non-commutative 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.
"Joint convergence of several copies of different patterned random matrices." Electron. J. Probab. 17 1 - 33, 2012. https://doi.org/10.1214/EJP.v17-1970