New Analytical Results for Poissonian and non-Poissonian Statistics of
  Cosmic Voids
  Stereology allows shifting from the 3D distribution of the volumes of
Poissonian Voronoi Diagrams to their 2D cross-sections. The basic assumption is
that the 3D statistics of the volumes of the voids in the local Universe has a
distribution function of the gamma-type. The standard rule of conversion from
3D volumes to 2D circles, adopting the standard rules of stereology, produces a
new probability density function of the radii which contains the Meijer
$G$-function. A non-Poissonian distribution of volumes is also considered. The
distribution of the 3D radii of the Sloan Digital Sky Survey Data Release 7 is
best fitted by a non-Poissonian distribution in volumes as given by the Kiang
function with argument of about two.
