Results dealing with the behavior of the integrated density of states of random divergence operators

In this paper we generalize and improve results proven for acoustic operators in \cite{jmp,long}. It deals with the behavior of the integrated density of states of random divergence operators of the form $H\mathrm{\_}\omega =\sum \mathrm{\_}{i,j=1}^d\mathrm{\partial }\mathrm{\_}x\mathrm{\_}ia\mathrm{\_}i,j(\omega ,x)\mathrm{\partial }\mathrm{\_}x\mathrm{\_}j$ ; on the internal band edges of the spectrum. We propose an application of such a result to get localization.