  It has been shown that, if a model displays long-range (power-law) spatial
correlations, its equal-time correlation matrix of this model will also have a
power law tail in the distribution of its high-lying eigenvalues. The purpose
of this letter is to show that the converse is generally incorrect: a power-law
tail in the high-lying eigenvalues of the correlation matrix may exist even in
the absence of equal-time power law correlations in the original model. We may
therefore view the study of the eigenvalue distribution of the correlation
matrix as a more powerful tool than the study of correlations, one which may in
fact uncover structure, that would otherwise not be apparent. Specifically, we
show that in the Totally Asymmetric Simple Exclusion Process, whereas there are
no clearly visible correlations in the steady state, the eigenvalues of its
correlation matrix exhibit a rich structure which we describe in detail.
