Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{ \infty-}(\Omega,{ \mathcal F},{ \mathbb P}) \otimes M_d({ \mathcal A})$ where $(\Omega,{ \mathcal F},{ \mathbb P})$ is a classical probability space and $({ \mathcal A},\varphi)$ is a non-commutative probability space. A central limit theorem for the mean $M_d(\mathbb{ C})$-valued moments of these random operator-valued matrices is derived. Also a numerical algorithm to compute the mean $M_d({ \mathbb C})$-valued Cauchy transform of operator-valued semicircular mixtures is analyzed.
Categories: math.PR math.OA