  Exact eigenvalue correlation functions are computed for large $N$ hermitian
one-matrix models with eigenvalues distributed in two symmetric cuts. An
asymptotic form for orthogonal polynomials for arbitrary polynomial potentials
that support a $Z_2$ symmetric distribution is obtained. This results in an
exact explicit expression for the kernel at large $N$ which determines all
eigenvalue correlators. The oscillating and smooth parts of the two point
correlator are extracted and the universality of local fine grained and
smoothed global correlators is established.
