  We consider orthogonal, unitary, and symplectic ensembles of random matrices
with (1/a)(ln x)^2 potentials, which obey spectral statistics different from
the Wigner-Dyson and are argued to have multifractal eigenstates. If the
coefficient $a$ is small, spectral correlations in the bulk are universally
governed by a translationally invariant, one-parameter generalization of the
sine kernel. We provide analytic expressions for the level spacing distribution
functions of this kernel, which are hybrids of the Wigner-Dyson and Poisson
distributions. By tuning the single parameter, our results can be excellently
fitted to the numerical data for three symmetry classes of the
three-dimensional Anderson Hamiltonians at the metal-insulator transition,
previously measured by several groups using exact diagonalization.
