On the Law of Addition of Random Matrices
  Normalized eigenvalue counting measure of the sum of two Hermitian (or real symmetric) matrices $A_{n}$ and $B_{n}$ rotated independently with respect to each other by the random unitary (or orthogonal) Haar distributed matrix $U_{n}$ (i.e. $A_{n}+U_{n}^{\ast}B_{n}U_{n}$) is studied in the limit of large matrix order $n$. Convergence in probability to a limiting nonrandom measure is established. A functional equation for the Stieltjes transform of the limiting measure in terms of limiting eigenvalue measures of $A_{n}$ and $B_{n}$ is obtained and studied.   Keywords: random matrices, eigenvalue distribution 
L. Pastur (1 and 3), V. Vasilchuk (2 and 3) ((1) Centre de Physique   Th\'eorique de CNRS, Luminy, Marseille, France, (2) U....