Operator-valued free multiplicative convolution: analytic subordination   theory and applications to random matrix theory
  We give an explicit description, via analytic subordination, of free multiplicative convolution of operator-valued distributions. In particular, the subordination function is obtained from an iteration process. This algorithm is easily numerically implementable. We present two concrete applications of our method: the product of two free operator-valued semicircular elements and the calculation of the distribution of $dcd+d^2cd^2$ for scalar-valued $c$ and $d$, which are free. Comparision between the solution obtained by our methods and simulations of random matrices shows excellent agreement. 
Serban T. Belinschi, Roland Speicher, John Treilhard, and Carlos   Vargas
math.OA math.PR