  We investigate linear matter density perturbations in models of structure
formation with causal seeds. Under the fluid approximation, we obtain the
analytic solutions using Green-function technique. Some incorrect solutions in
the literature are corrected here. Based on this, we analytically prove that
the matter density perturbations today are independent of the way the causal
seeds were compensated into the background contents of the universe when they
were first formed. We also find that the compensation scale depends not only on
the dynamics of the universe, but also on the properties of the seeds near the
horizon scale. It can be accurately located by employing our Green-function
solutions.
