Spectral universality of real chiral random matrix ensembles

We investigate the universality of microscopic eigenvalue correlations for random matrix theories with the global symmetries of the QCD partition func tion. In this article we analyze the case of real valued chiral random matr ix theories (beta = 1) by relating the kernel of the correlations functions for beta = 1 to the kernel of chiral random matrix theories with complex m atrix elements (beta = 2), which is already known to be universal. We show universality based on a novel asymptotic property of the skew-orthogonal po lynomials: an integral over the corresponding wavefunctions oscillates abou t half its asymptotic value in the region of the bulk of the zeros. This re sult solves the puzzle that microscopic universality persists in spite of c ontributions to the microscopic correlators from the region near the larges t zero of the skew-orthogonal polynomials. Our analytical results are illus trated by the numerical construction of the skew-orthogonal polynomials for an x(4) probability potential. (C) 2000 Elsevier Science B.V. All rights r eserved.