  We investigate the properties of sparse matrix ensembles with particular
regard for the spectral ergodicity hypothesis, which claims the identity of
ensemble and spectral averages of spectral correlators. An apparent violation
of the spectral ergodicity is observed. This effect is studied with the aid of
the normal modes of the random matrix spectrum, which describe fluctuations of
the eigenvalues around their average positions. This analysis reveals that
spectral ergodicity is not broken, but that different energy scales of the
spectra are examined by the two averaging techniques. Normal modes are shown to
provide a useful complement to traditional spectral analysis with possible
applications to a wide range of physical systems.
