We study a rotating Bose-Einstein condensate in a homogeneous trap in
the framework of the Gross-Pitaevskii theory above the first critical
speed, i.e., we consider the regime with many vortices but a density
close to the vortex-free prole. We prove that the vortex distribution
of the ground state is not uniform and is given by an explicit measure
minimizing a suitable renormalized energy.