  We compute the asymptotic temporal behavior of the dynamical complexity
associated with the maximum probability trajectories on Gaussian statistical
manifolds in presence of correlations between the variables labeling the
macrostates of the system. The algorithmic structure of our asymptotic
computations is presented and special focus is devoted to the diagonalization
procedure that allows to simplify the problem in a remarkable way. We observe a
power law decay of the information geometric complexity at a rate determined by
the correlation coefficient. We conclude that macro-correlations lead to the
emergence of an asymptotic information geometric compression of the statistical
macrostates explored on the configuration manifold of the model in its
evolution between the initial and final macrostates.
