LOCALIZATION IN ENSEMBLE OF SPARSE RANDOM MATRICES

We study a transition from the localized to the delocalized phase in a novel sparse-random-matrices (SRM) ensemble. Within the scope of a supersymmetric approach it can be described by an order-parameter function. We attribute a clear physical meaning of this function providing a link between our approach and other methods. Equations for a "mobility edge" and "inverse participation ratio" are derived. Some analogies between the SRM model and mean-field theory of spin glass as well as possible applications to the theory of Anderson localization are discussed.