We study statistical properties of the ensemble of large N x N random matrices whose entries H-ij decrease in a power-law fashion H-ij similar to i-j(-alpha). Mapping the problem onto a nonlinear a model with nonlocal interaction, we find a transition from localized to extended states at alpha=1. At this critical value of alpha the system exhibits multifractality and spectral statistics intermediate between the Wigner-Dyson and Poisson statistics. These features are reminiscent of those typical of the mobility edge of disordered conductors. We find a continuous set of critical theories at alpha=1, parametrized by the value of the coupling constant of the sigma model. At alpha>1 all states are expected to be localized with integrable power-law tails. At the same time, for 1展开▼
