  In this article we study the problem of localization of eigenvalues for the
non-homogeneous hierarchical Anderson model. More specifically, given the
hierarchical Anderson model with spectral dimension $0<d<1$ with a random
potential acting on the diagonal of non i.i.d. random variables, sufficient
conditions on the disorder are provided in order to obtain the two main
results: the weak convergence of the counting measure for almost all
realization of the random potential and the weak convergence of the re-scaled
eigenvalue counting measure to a Poisson point process. The technical part
improves the already existing arguments of Kritchevski , who studied the
hierarchical model with a disorder acting on the diagonal, with independent and
identically distributed random variables, by using the argument of Minami . At
the end of this article, we study an application example that allows us to
understand some relations between the spectral dimension of the hierarchical
Laplacian and the magnitude of the disorder.
