  A method of resummation of infinite series of perturbation theory diagrams is
applied for studying the properties of random band matrices. The topological
classification of Feynman diagrams, which was actively used in last years for
matrix model regularization of 2d-gravity, turns out to be very useful for band
matrices. The critical behavior at the edge of spectrum and the asymptotics of
energy level correlation function are considered. This correlation function
together with the hypothesis about universality of spectral correlations allows
to estimate easily the localization length for eigen-vectors. A smoothed
two-point correlation function of local density of states $\overline{
\rho(E_1,i) \rho(E_2,j)_c}$ as well as the energy level correlation for finite
size band matrices are also found. As d-dimensional generalization of band
matrices lattice Hamiltonians with long-range random hopping are considered as
well.
