  We present improved upper and lower bounds for the momentum-space ghost
propagator of Yang-Mills theories in terms of the two smallest nonzero
eigenvalues (and their corresponding eigenvectors) of the Faddeev-Popov matrix.
These results are verified using data from four-dimensional numerical
simulations of SU(2) lattice gauge theory in minimal Landau gauge at beta =
2.2, for lattice sides N = 16, 32, 48 and 64. Gribov-copy effects are discussed
by considering four different sets of numerical minima. We then present a lower
bound for the smallest nonzero eigenvalue of the Faddeev-Popov matrix in terms
of the smallest nonzero momentum on the lattice and of a parameter
characterizing the geometry of the first Gribov region $\Omega$. This allows a
simple and intuitive description of the infinite-volume limit in the ghost
sector. In particular, we show how nonperturbative effects may be quantified by
the rate at which typical thermalized and gauge-fixed configurations approach
the boundary of Omega, known as the first Gribov horizon. As a result, a simple
and concrete explanation emerges for why lattice studies do not observe an
enhanced ghost propagator in the deep infrared limit. Most of the simulations
have been performed on the Blue Gene/P--IBM supercomputer shared by Rice
University and S\~ao Paulo University.
