Microscopic universality of complex matrix model correlation functions at weak non-Hermiticity

TL;DR

This paper proves the universality of microscopic correlation functions in complex matrix models with weak non-Hermiticity, showing they are independent of the specific measure used, near the origin in the large matrix limit.

Contribution

It establishes the universality of correlation functions for a broad class of non-Gaussian measures in complex matrix models at weak non-Hermiticity, including cases with Dirac mass terms.

Findings

Universality of correlation functions near the origin in large-N limit.

Asymptotics of orthogonal polynomials in the complex plane are universal.

Mapping between massive and massless correlators confirms universality.

Abstract

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.