  We compute the large scale (macroscopic) correlations in ensembles of normal
random matrices with an arbitrary measure and in ensembles of general
non-Hermition matrices with a class of non-Gaussian measures. In both cases the
eigenvalues are complex and in the large $N$ limit they occupy a domain in the
complex plane. For the case when the support of eigenvalues is a connected
compact domain, we compute two-, three- and four-point connected correlation
functions in the first non-vanishing order in 1/N in a manner that the
algorithm of computing higher correlations becomes clear. The correlation
functions are expressed through the solution of the Dirichlet boundary problem
in the domain complementary to the support of eigenvalues. The two-point
correlation functions are shown to be universal in the sense that they depend
only on the support of eigenvalues and are expressed through the Dirichlet
Green function of its complement.
