  We solve the puzzle of the disagreement between orthogonal polynomials
methods and mean field calculations for random NxN matrices with a disconnected
eigenvalue support. We show that the difference does not stem from a Z2
symmetry breaking, but from the discreteness of the number of eigenvalues. This
leads to additional terms (quasiperiodic in N) which must be added to the naive
mean field expressions. Our result invalidates the existence of a smooth
topological large N expansion and some postulated universality properties of
correlators. We derive the large N expansion of the free energy for the general
2-cut case. From it we rederive by a direct and easy mean-field-like method the
2-point correlators and the asymptotic orthogonal polynomials. We extend our
results to any number of cuts and to non-real potentials.
