We summarize recent analytical results obtained for the discretization effects of the non-Hermitian Wilson
Dirac operator. We include the effect of all three leading low energy constants in our analysis. In particular we
discuss the results for the eigenvalue densities close to the continuum limit but we also consider the case of large lattice spacing which
is closely related to the mean field limit. Finally, we extract simple relations between measurable
spectral quantities and the low energy constants. These relations serve as a new way to measure the additional low energy constants of Wilson chiral perturbation theory.