  We use high-resolution N-body simulations, combined with a halo occupation
model of galaxy bias, to investigate voids in the galaxy distribution. Our goal
is to address the 'void phenomenon' of Peebles (2001), which presents the
observed dearth of faint galaxies in voids as a challenge to the current
cosmology. In our model, galaxy luminosity is determined only as a function of
dark matter halo mass. With this simple assumption, we demonstrate that large,
empty voids of ~15 Mpc/h in diameter are expected even for galaxies seven
magnitudes fainter than L*. The predictions of our model are in excellent
agreement with several statistical measures; (i) the luminosity function of
galaxies in underdense regions, (ii) nearest neighbor statistics of dwarf
galaxies, (iii) the void probability function of faint galaxies. In the
transition between filaments and voids in the dark matter, the halo mass
function changes abruptly, causing the maximum galaxy luminosity to decrease by
~5 magnitudes over a range of ~1 Mpc/h. Thus the boundary between filaments and
voids in the galaxy distribution is nearly as sharp for dwarfs as for ~L*
objects. These results support a picture in which galaxy formation is driven
predominantly by the mass of the host dark matter halo, and is nearly
independent of the larger-scale halo environment. Further, they demonstrate
that LCDM, combined with a straightforward bias model, naturally explains the
existence of the void phenomenon.
