Logarithmic universality in random matrix theory

Universality in unitary invariant random matrix ensembles with complex matr ix elements is considered. We treat two general ensembles which have a dete rminant factor in the weight. These ensembles are relevant, e.g., for spect ra of the Dirac operator in QCD. In addition to the well established univer sality with respect to the choice of potential, we prove that microscopic s pectral correlators are unaffected when the matrix in the determinant is re placed by an expansion in powers of the matrix. We refer to this invariance as logarithmic universality. The result is used in proving that a simple r andom matrix model with Ginsparg-Wilson symmetry has the same microscopic s pectral correlators as chiral random matrix theory. (C) 1999 Elsevier Scien ce B.V. All rights reserved.