  We study force correlations in the q-model for granular media at infinite
depth, for general q-distributions. We show that there are no 2-point force
correlations as long as q-values at different sites are uncorrelated. However,
higher order correlations can persist, and if they do, they only decay with a
power of the distance. Furthermore, we find the entire set of q-distributions
for which the force distribution factorizes. It includes distributions ranging
from infinitely sharp to almost critical. Finally, we show that 2-point force
correlations do appear whenever there are correlations between q-values at
different sites in a layer; various cases are evaluated explicitly.
