  We study numerically and analytically a simple off-lattice model of scalar
harmonic vibrations by means of Euclidean random matrix theory. Since the
spectrum of this model shares the most puzzling spectral features with the
high-frequency domain of glasses (non-Rayleigh broadening of the Brillouin
peak, boson peak and secondary peak), the Euclidean random matrix theory
provide a single and fairly simple theoretical framework to their explanation.
