Spectral properties of the overlap Dirac operator in QCD

We discuss the eigenvalue distribution of the overlap Dirac operator in quenched QCD on lattices of size 84 , 104 and 124 at β = 5.85 and β = 6. We distinguish the topological sectors and study the distributions of the leading non-zero eigenvalues, which are stereographically mapped onto the imaginary axis. Thus they can be compared to the predictions of random matrix theory applied to the ε -expansion of chiral perturbation theory. We find a satisfactory agreement, if the physical volume exceeds about (1.2 fm)4 . For the unfolded level spacing distribution we find an accurate agreement with the random matrix conjecture on all volumes that we considered. (author)