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.