On the Distribution of Products of Spherical Classes in Classical   Symmetric Spaces of Rank One
  The distribution of products of random matrices chosen from fixed spherical classes is determined for classical rank 1 symmetric spaces. It is observed that $n\to\infty$ limit behaves approximately as in the abelian case. A theorem on the rate of convergence to the Haar measure in the case of SU(n) is also established. 
Jafar Shaffaf