  The microscopic correlation functions of non-chiral random matrix models with
complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In
the large-N limit of weak non-Hermiticity, where N is the size of the complex
matrices, we can prove that all k-point correlation functions including an
arbitrary number of Dirac mass terms are universal close to the origin. To this
aim we establish the universality of the asymptotics of orthogonal polynomials
in the complex plane. The universality of the correlation functions then
follows from that of the kernel of orthogonal polynomials and a mapping of
massive to massless correlators.
