  The asymmetric simple inclusion process (ASIP) --- a lattice-gas model for
unidirectional transport with irreversible aggregation --- has been proposed as
an inclusion counterpart of the asymmetric simple exclusion process and as a
batch service counterpart of the tandem Jackson network. To date, analytical
tractability of the model has been limited: while the average particle density
in the model is easy to compute, very little is known about its joint occupancy
distribution. To partially bridge this gap, we study occupancy correlations in
the ASIP. We take an analytical approach to this problem and derive an exact
formula for the covariance matrix of the steady-state occupancy vector. We
verify the validity of this formula numerically in small ASIP systems, where
Monte-Carlo simulations can provide reliable estimates for correlations in
reasonable time, and further use it to draw a comprehensive picture of spatial
occupancy correlations in ASIP systems of arbitrary size.
