A hierarchy of voids: More ado about nothing
  We extend earlier work on the problem of estimating the void-volume function
-- the abundance and evolution of large voids which grow gravitationally in an
expanding universe -- in two ways. The first removes an ambiguity about how the
void-in-cloud process, which erases small voids, should be incorporated into
the excursion set approach. The main technical change here is to think of voids
within a fully Eulerian, rather than purely Lagrangian, framework. The second
accounts for correlations between different spatial scales in the initial
conditions. We provide numerical and analytical arguments showing how and why
both changes modify the predicted abundances substantially. In particular, we
show that the predicted importance of the void-in-cloud process depends
strongly on whether or not one accounts for correlations between scales. With
our new formulation, the void-in-cloud process dramatically reduces the
predicted abundances of voids if such correlations are ignored, but only
matters for the smallest voids in the more realistic case in which the spatial
correlations are included.
