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

G. Akemann, P. H. Damgaard, U. Magnea, S. Nishigaki

Published 1996-09-22, updated 1996-09-23Version 2

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.