Asymptotic behavior of the density of states on a random lattice

We study the diffusion of a particle on a random lattice with fluctuating local connectivity of average value q. This model is a basic description of relaxation processes in random media with geometrical defects. We analyze here the asymptotic behavior of the eigenvalue distribution for the Laplacian operator. We found that the localized states outside the mobility band and observed by Biroli and Monasson (1999, J. Phys. A: Math. Gen. 32 L255), in a previous numerical analysis, are described by saddle point solutions that breaks the rotational symmetry of the main action in the real space. The density of states is characterized asymptotically by a series of peaks with periodicity 1/q.