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arXiv · 1209.4759

New Analytical Results for Poissonian and non-Poissonian Statistics of Cosmic Voids

L. Zaninetti
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Abstract

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.

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L. Zaninetti. 2012-09-21. New Analytical Results for Poissonian and non-Poissonian Statistics of Cosmic Voids. https://arxiv.org/abs/1209.4759

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