GranMa 2011Oct 3  6, 2011Institut Henri Poincaré, Paris 

Gernot Akemann, Bielefeld University: A New TwoMatrix Model and the Wilson Dirac OperatorWe introduce and solve a new random twomatrix model that describes the transition from the chiral Gaussian Unitary Ensemble to the Gaussian Unitary Ensemble, and generalisations thereof. The motivation for this study is to describe the effect of finite lattice spacing close to the continuum in Lattice Gauge Theory. The Hermitian version of the QCD Dirac operator discretised a la Ken Wilson is mapped to a random matrix which contains a chiral part (at zero lattice spacing) and a part that breaks this symmetry. In order to compute all its spectral correlations functions we first compute the joint probability density, given by a Pfaffian times a Vandermonde. This setting can be solved efficiently using skeworthogonal polynomials, and we give explicit formula at finite N and in the infiniteN limit at weak nonchirality. We also discuss some open problems and relations to other models. Go to the GranMa home page. 