Strong eigenfunction correlations near the Anderson-localization transition

We study the overlap of two different eigenfunctions as compared with self-overlap in the framework of an infinite-dimensional version of the disordered tight-binding model. Despite a very sparse structure of the eigenstates in the vicinity of the Anderson transition, their mutual overlap is still found to be of the same order as self-overlap as long as the energy separation is smaller than a critical value. The latter fact explains the robustness of the Wigner-Dyson level statistics everywhere in the phase of extended states. The same picture is expected to hold for usual d-dimensional conductors, ensuring the s^B form of the level repulsion at a critical point.