PUB - Publikationen an der Universität Bielefeld

We introduce a random two-matrix model interpolating between a chiralHermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix withoutsymmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE)and Gaussian Unitary Ensemble (GUE), respectively. In the microscopic large-nlimit in the vicinity of the chGUE (which we denote by weakly non-chiral limit)this theory is in one to one correspondence to the partition function of Wilsonchiral perturbation theory in the epsilon regime, such as the related twomatrix-model previously introduced in refs. [20,21]. For a generic number offlavours and rectangular block matrices in the chGUE part we derive aneigenvalue representation for the partition function displaying a Pfaffianstructure. In the quenched case with nu=0,1 we derive all spectral correlationsfunctions in our model for finite-n, given in terms of skew-orthogonalpolynomials. The latter are expressed as Gaussian integrals over standardLaguerre polynomials. In the weakly non-chiral microscopic limit this yieldsall corresponding quenched eigenvalue correlation functions of the HermitianWilson operator.