Abstract

ZANINETTI, L.. New Analytic Results for Poissonian and non-Poissonian Statistics of Cosmic Voids. Rev. mex. astron. astrofis [online]. 2012, vol.48, n.2, pp.209-222. ISSN 0185-1101.

Stereology allows shifting from the 3D distribution of the volumes of Poisso-nian 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.

Keywords : galaxies; clusters [general]; galaxies [statistics]; galaxies [large-scale structure of universe]; methods [statistical].