Random unitaries in non-commutative tori, and an asymptotic model for   q-circular systems
  We consider the concept of a q-circular system, which is a deformation of the circular system from free probability, taking place in the framework of the so-called 'q-commutation relations'. We show that certain averages of random unitaries in non-commutative tori behave asymptotically like a q-circular system. 
James A. Mingo and Alexandru Nica