Random negative-U hubbard model

In the case of superconductors whose electrons attract each other only if t hey are near certain centers, the question arises of how many such centers are needed to make the ground state superconducting? We shall examine it in the context of a random U Hubbard model. In short, we study the case where U-i is - \U\ and 0 with probability c and 1-c, respectively, on a lattice whose sites are labeled i using the Gorkov decoupling and the coherent pote ntial approximation. We argue that for this model there is a critical conce ntration co below which the system is not a superconductor.