Quantum random walks and their convergence

Using coordinate-free basic operators on toy Fock spaces cite{AP}, quantum random walks are defined following the ideas in cite{LP,AP}. Strong convergence of quantum random walks associated with bounded structure maps is proved under suitable assumptions, extendings the result obtained in cite{KBS} in case of one dimensional noise. To handle infinite dimensional noise we have used the coordinate-free language of quantum stochastic calculus developed in cite{GS1}.