Universality of random matrices in the microscopic limit and the Dirac operator spectrum

Abstract

We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant orthogonal polynomials into a Bessel equation governing the local asymptotics around the origin. The possible physical interpretation as the universality of soft spectrum of the Dirac operator is briefly discussed.

18 pages, LaTeX. One reference added

References in corpus (10)

• Random matrix theory and spectral sum rules for the Dirac operator in QCD
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
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