  Lattice fermions in a fluctuating gauge field can show localization, much
like electrons in a disordered potential. We study the spectrum of localized
and extended states of supercritical Wilson fermions in gauge ensembles
generated with plaquette and improved actions. When the Wilson fermion operator
is used to construct the overlap kernel, the mobility edge, that is the
boundary between the localized and extended states, determines the range of the
kernel.
