Asymptotic matricial models and QWEP property for q-Araki-Woods von Neumann algebras

Using Speicher central limit Theorem we provide Hiai’s q-Araki-Woods von Neumann algebras with nice asymptotic matricial models. Then, we use this model and an elaborated ultraproduct procedure, to show that all q-Araki-Woods von Neumann algebras are QWEP.