  The low-temperature properties of glasses present important differences with
respect to crystalline matter. In particular, models such as the Debye model of
solids, which assume the existence of an underlying regular lattice, predict
that the specific heat of solids varies with the cube of temperature at low
temperatures. Since the 1970s' at least, it is a well established experimental
fact that the specific heat of glasses is instead just linear in $T$ at $T \sim
1K$, and presents a pronounced peak when normalized by $T^{3}$, known as the
boson peak. Here we present a new approach which suggests that the vibrational
and thermal properties of amorphous solids are affected by the random matrix
part of the vibrational spectrum. The model is also able to reproduce, for the
first time, the experimentally observed inverse proportionality between the
boson peak in the specific heat and the shear modulus.
