| Abstract: | The mechanical, dynamical and thermodynamical properties of amorphous solids are far less understood than those of crystalline solids. The analysis of these systems is complicated due to the presence of emerging disorder and vastly different interaction strengths between the constituents of these materials. In this talk, I will focus on the elasticity. More precisely I will look at spectral properties of random elastic networks and argue in which sense they provide a good toy model of disordered solids. Using the Cavity method, a sort of Bethe-Peierls iterative method, in the limit of small heterogeneities of the graph connectivity, I will derive approximate analytical expressions for the spectral density of such graphs. Finally, I will point out implications of these result on the macroscopic properties of amorphous solids. |