Phonons in random elastic media and the boson peak

We show that the density of states of random wave equations, normalized by the square of the frequency, has a peak-sometimes narrow and sometimes broad-in the range of wave vectors between the disorder correlation length and the interatomic spacing. We arrive at this conclusion by examining the low and high-frequency asymptotics of the density of states. The results of this letter may be relevant for understanding vibrational spectra and light propagation in disordered solids.