  We prove that for Gaussian random normal matrices the correlation function
has universal behavior.
  Using the technique of orthogonal polynomials and identities similar to the
Christoffel-Darboux formula, we find that in the limit, as the dimension of the
matrix tends to infinity, the density of eigenvalues converges to a constant
inside of an ellipse and to zero outside. The convergence holds locally
uniformly. At the boundary, in scaled coordinates holding the distance between
eigenvalues constant, we show that the density is falling off to zero like the
complementary error function. The convergence is uniform on the boundary.
Further we give an explicit expression for the the correlation function.
