Holomorphic matrix integrals Original Research Article

We study a class of holomorphic matrix models. The integrals are taken over middle-dimensional cycles in the space of complex square matrices. As the size of the matrices tends to infinity, the distribution of eigenvalues is given by a measure with support on a collection of arcs in the complex planes. We show that the arcs are level sets of the imaginary part of a hyperelliptic integral connecting branch points.