  It recently has been found that methods of the statistical theories of
spectra can be a useful tool in the analysis of spectra far from levels of
Hamiltonian systems. Several examples originate from areas, such as
quantitative linguistics and polymers. The purpose of the present study is to
deepen this kind of approach by performing a more comprehensive spectral
analysis that measures both the local and long-range statistics. We have found
that, as a common feature, spectra of this kind can exhibit a situation in
which local statistics are relatively quenched while the long range ones show
large fluctuations. By combining extensions of the standard Random Matrix
Theory (RMT) and considering long spectra, we demonstrate that this phenomenon
occurs when weak disorder is introduced in a RMT spectrum or when strong
disorder acts in a Poisson regime. We show that the long-range statistics
follow the Taylor law, which suggests the presence of a fluctuation scaling
(FS) mechanism in this kind of spectra.
