Spatial correlations in exclusion models corresponding to the zero-range process

We show that the steady state weights of all one-dimensional exclusion models which are mapped to the zero-range process (ZRP) can be written in a matrix product form, where the required matrices depend only on the steady state weights of the ZRP. An infinite-dimensional representation of these matrices which works for generic systems has also been provided. This is in contrast to the case for the usual matrix product ansatz which does not always guarantee a solution for the dynamics dependent algebra that the matrices need to satisfy. The formulation helps us study the spatial correlations of these exclusion processes which are unfeasibly difficult to obtain directly from their ZRP correspondence. To illustrate this method we reproduce certain known results, and then investigate unexplored correlations in some other model systems. (letter)