# Large N expansion for normal and complex matrix ensembles

## Anton Zabrodin

**Abstract: **

We will discuss the nature of subleading terms in the 1/N (genus) expansion
of the free energy for ensembles of normal and complex

random matrices. The results are expressed through geometric and spectral
properties of the support of eigenvalues. In particular,

the O(1)-term is given by the regularized determinant of the Laplace
operator in the complementary domain with Dirichlet boundary

conditions.