The density of vibrational states g(ω) of an amorphous system is studied by using the random-matrix theory. Taking into account the most important correlations between elements of the random matrix of the system, equations for the density of vibrational states g(ω) are obtained. The analysis of these equations shows that in the low-frequency region the vibrational density of states has the Debye behavior g(ω) ～ ω~2. In the higher frequency region, there is the boson peak as an additional contribution to the density of states. The obtained equations are in a good agreement with the numerical results and allow us to find an exact shape of the boson peak.
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