  We have considered a disordered driven-diffusive system defined on a ring.
This system can be mapped onto a heterogeneous zero-range process. We have
shown that the grand-canonical partition function of this process can be
obtained using a matrix product formalism and that it is exactly equal to the
partition function of a two-dimensional walk model. The canonical partition
function of this process is also calculated. Two simple examples are presented
in order to confirm the results.
