This work is at the crossroads of operator algebra andnon-commutative probability theories. Some properties of$\Gamma_{q}(H_{\R})$ are investigated, where $\Gamma_{q}(H_{\R})$stands for the von Neumann algebra generated by non-commutative$q$-deformed Gaussian variables . These variables are given asoperators acting on a $q-$deformed Fock space where the$q$-canonical commutation relations are realized by non-commutativeshift operators.Some $L^{\infty}$-Khintchin type inequalities with operatorcoefficients, concerning Wick products of a given length, arediscussed and established in the first chapter. These inequalitiesextend, on the one hand Haagerup's scalar inequalities in the freecase and, on the other hand Bo.zejko and Speicher's operatorcoefficients inequalities for $q$-Gaussians. From those inequalitiesfollows the non-injectivity of $\Gamma_{q}(H_{\R})$ as soon as$\dim_{\R}(H_{\R})> 1$.The second chapter is devoted to the construction of an asymptoticmatricial model for $q$-Gaussian variables. Such a model is thenused to prove that all $q$-Gaussian algebras are QWEP.The $C^*-$algebraic case is also investigated and, the precedingresults are studied and stated for various other generalized$q$-Gaussian algebras such as type $I!I!I$ $q$-Gaussian algebrasand $T-$deformed Gaussian algebras where $T$ is a Yang-Baxteroperator.
