  Through simple analytical calculations and numerical simulations, we
demonstrate the generic existence of a self-organized macroscopic state in any
large multivariate system possessing non-vanishing average correlations between
a finite fraction of all pairs of elements. The coexistence of an eigenvalue
spectrum predicted by random matrix theory (RMT) and a few very large
eigenvalues in large empirical correlation matrices is shown to result from a
bottom-up collective effect of the underlying time series rather than a
top-down impact of factors. Our results, in excellent agreement with previous
results obtained on large financial correlation matrices, show that there is
relevant information also in the bulk of the eigenvalue spectrum and
rationalize the presence of market factors previously introduced in an ad hoc
manner.
