Quantifying galactic clustering and departures from randomness of the inter-galactic void probability function using information geometry

Abstract

We study a family of parametric statistical models based on gamma distributions, which do give realistic descriptions for other stochastic porous media. Gamma distributions contain as a special case the exponential distributions, which correspond to the `random' void size probability arising from Poisson processes. The space of parameters is a surface with a natural Riemannian metric structure. This surface contains the Poisson processes as an isometric embedding and a recent theorem shows that it contains neighbourhoods of all departures from randomness. The method provides thereby a geometric setting for quantifying departures from randomness and on which may be formulated cosmological evolutionary dynamics for galactic clustering and for the concomitant development of the void size distribution. The 2dFGRS data offer the possibility of more detailed investigation of this approach than was possible when it was originally suggested and some parameter estimations are given.