  We consider homogeneous open quantum random walks on a lattice with finite
dimensional local Hilbert space and we study in particular the position process
of the quantum trajectories of the walk. We prove that the properly rescaled
position process asymptotically approaches a mixture of Gaussian measures. We
can generalize the existing central limit type results and give more explicit
expressions for the involved asymptotic quantities, dropping any additional
condition on the walk. We use deformation and spectral techniques, together
with reducibility properties of the local channel associated with the open
quantum walk. Further, we can provide a large deviations' principle in the case
of a fast recurrent local channel and at least lower and upper bounds in the
general case.
