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Since the 90's random matrix theory (RMT) was successfully applied to quantum chromodynamics (QCD). In particular the low lying spectrum of the Dirac operator can be exactly mapped to chiral RMT. The same applies to lattice QCD. One particular modification of the Dirac operator on the lattice is the one introduced by Wilson. This modification explicitly breaks chiral symmetry even though the quark masses are set to zero. Recently a random matrix model was introduced which lies in the same universality class as the Wilson-Dirac operator. The aim is to investigate the lattice artifacts in data of lattice simulations with RMT as strongly simplified model. Quite recently we derived the joint probability density and, in particular, the level density of the so called Wilson random matrix ensemble. I will present these new results in my talk. Moreover I will show that the Wilson random matrix ensemble lies in a new class of ensembles related to a mixing of orthogonal and skew-orthogonal polynomials. Hence it is a new kind of interpolations between universality classes.

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Mario Kieburg, Stony Brook University
Seminarraum Theoretische Physik
Contact: not specified