  We present rigorous upper and lower bounds for the momentum-space ghost
propagator G(p) of Yang-Mills theories in terms of the smallest nonzero
eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix.
We apply our analysis to data from simulations of SU(2) lattice gauge theory in
Landau gauge, using the largest lattice sizes to date. Our results suggest
that, in three and in four space-time dimensions, the Landau-gauge ghost
propagator is not enhanced as compared to its tree-level behavior. This is also
seen in plots and fits of the ghost dressing function. In the two dimensional
case, on the other hand, we find that G(p) diverges as p^{-2-2 kappa} with
kappa \approx 0.15, in agreement with Ref. [1]. We note that our discussion is
general, although we make an application only to pure gauge theory in Landau
gauge. Most of our simulations have been performed on the IBM supercomputer at
the University of Sao Paulo.
