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

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

2002-06-11

arxiv.org/abs/hep-th/0206086v1

Phys.Lett. B547 (2002) 100-108

Physics

High Energy Physics

High Energy Physics - Theory

13 pages

Scientific paper

10.1016/S0370-2693(02)02737-5

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.

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