  The density of vibrational states for glasses and jammed solids exhibits
universal features, including an excess of modes above the Debye prediction
known as the boson peak located at a frequency $\omega^*$ . We show that the
eigenvector statistics for boson peak modes are universal, and develop a new
definition of the boson peak based on this universality that displays the
previously observed characteristic scaling $\omega^*\sim p^{-1/2}$ . We
identify a large new class of random matrices that obey a generalized global
tranlational invariance constraint and demonstrate that members of this class
also have a boson peak with precisely the same universal eigenvector
statistics. We denote this class as boson peak random matrices, and conjecture
it comprises a new universality class. We characterize the eigenvector
statistics as a function of coordination number, and find that one member of
this new class reproduces the scaling of $\omega^{*}$ with coordination number
that is observed near the jamming transition.
