  We study the spectrum of a system of coupled disordered harmonic oscillators
in the thermodynamic limit. This Euclidean random matrix ensemble has been
suggested as model for the low-temperature vibrational properties of glass.
Exact numerical diagonalization is performed in three and two spatial
dimensions, which is accompanied by a detailed finite size analysis. It reveals
a low-frequency regime of sound waves that are damped by Rayleigh scattering.
At large frequencies localized modes exist. In between, the central peak in the
vibrational density of states is well described by Wigner's semicircle law for
not too large disorder, as is expected for simple random matrix systems. We
compare our results with predictions from two recent self-consistent field
theories.
