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We present improved upper and lower bounds for the momentum-space ghostpropagator of Yang-Mills theories in terms of the two smallest nonzeroeigenvalues (and their corresponding eigenvectors) of the Faddeev-Popov matrix.These results are verified using data from four-dimensional numericalsimulations 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 discussedby considering four different sets of numerical minima. We then present a lowerbound for the smallest nonzero eigenvalue of the Faddeev-Popov matrix in termsof the smallest nonzero momentum on the lattice and of a parametercharacterizing the geometry of the first Gribov region $\Omega$. This allows asimple and intuitive description of the infinite-volume limit in the ghostsector. In particular, we show how nonperturbative effects may be quantified bythe rate at which typical thermalized and gauge-fixed configurations approachthe boundary of Omega, known as the first Gribov horizon. As a result, a simpleand concrete explanation emerges for why lattice studies do not observe anenhanced ghost propagator in the deep infrared limit. Most of the simulationshave been performed on the Blue Gene/P--IBM supercomputer shared by RiceUniversity and S\~ao Paulo University.

Ghost sector and geometry in minimal Landau gauge: further constraining the infinite-volume limit