2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/135551We 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.32 pages, LaTeX 2.09Operator AlgebrasProbability46L50, 81S25text