  We consider the effect of discretization errors on the microscopic spectrum
of the Wilson Dirac operator using both chiral Perturbation Theory and chiral
Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the
microscopic spectral density of the Hermitian Wilson Dirac operator as well as
the distribution of the chirality over the real eigenvalues of the Wilson Dirac
operator. It is shown that a chiral Random Matrix Theory for the Wilson Dirac
operator reproduces the leading zero-momentum terms of Wilson chiral
Perturbation Theory. All results are obtained for fixed index of the Wilson
Dirac operator. The low-energy constants of Wilson chiral Perturbation theory
are shown to be constrained by the Hermiticity properties of the Wilson Dirac
operator.
