Spectral ergodicity and normal modes in ensembles of sparse matrices

We investigate the properties of sparse-matrix ensembles with particular re gard for the spectral ergodicity hypothesis, which claims the identity of e nsemble and spectral averages of spectral correlators. An apparent violatio n of the spectral ergodicity is observed. This effect is studied with the a id of the normal modes of the random-matrix spectrum, which describe fluctu ations of the eigenvalues around their average positions. This analysis rev eals that spectral ergodicity is not broken, but that different energy scal es of the spectra are examined by the two averaging techniques. Normal mode s are shown to provide a useful complement to traditional spectral analysis with possible applications to a wide range of physical systems. (C) 2001 E lsevier Science B.V. All rights reserved.