Factorized steady states in mass transport models

We study a class of mass transport models where mass is transported in a preferred direction around a one-dimensional periodic lattice and is globally conserved. The model encompasses both discrete and continuous masses and parallel and random sequential dynamics and includes models such as the zero-range process and asymmetric random average process as special cases. We derive a necessary and sufficient condition for the steady state to factorize, which takes a rather simple form.