  The observed preponderance of ground states with angular momentum L=0 in
many-body quantum systems with random two-body interactions is analyzed in
terms of correlation coefficients (covariances) among different eigenstates. It
is shown that the geometric analysis of Chau {\it et al.} can be interpreted in
terms of correlations (covariances) between energy eigenvalues thus providing
an entirely statistical explanation of the distribution of ground state angular
momenta of randomly interacting quantum systems which, in principle, is valid
for both fermionic and bosonic systems. The method is illustrated for the
interacting boson model.
