  The local elastic properties of strongly disordered host material are
investigated using the theory of correlated random matrices. A significant
increase in stiffness is shown in the interfacial region, which thickness
depends on the strength of disorder. It is shown that this effect plays a
crucial role in nanocomposites, in which interfacial regions are formed around
each nanoparticle. The studied interfacial effect can significantly increase
the influence of nanoparticles on the macroscopic stiffness of nanocomposites.
The obtained thickness of the interfacial region is determined by the
heterogeneity length scale and is of the same order as the length scale of the
boson peak.
