Statistics of the galaxy distribution

The universe appears from recent observational results to be a highly structured but also highly disordered medium. This accounts for the difficulties with a conventional statistical approach. Since the statistics of disordered media is an increasingly well-studied field in physics, it is tempting to try to adapt its methods for the study of the universe (the use of correlation functions also resulted from the adaptation of techniques from a very different field to astrophysics). This is already the case for the fractal analysis, which, mainly developed in microscopic statistics, is increasingly used in astrophysics. I suggest a new approach, also derived from the study of disordered media, both from the study of percolation clusters and from the dynamics of so-called “cluster aggregation” gelification models. This approach is briefly presented. Its main interest lies in two points. First, it suggests an analysis able to characterize features of unconventional statistics (those that seem to be present in the galaxy distribution and which conventional indicators are unable to take into account). It appears alsoa priori very convenient for a synthetic approach, since it can be related to the other indicators used up to now: the link with the void probability function is very straightforward. The connexion with fractals can be said to be contained in the method, since the objects defined during this analysis are themselves fractal: different kinds of fractal dimensions are very easy to extract from the analysis. The link with the percolation studies is also very natural since the method is adapted from the study of percolation clusters. It is also expected that the information concerning the topology is contained in this approach; this seems natural since the method is very sensitive to the topology of the distribution and posses some common characteristics with the topology analysis already developed by Gottet al. (1986). The quantitative relations remain however to be calculated. Additionally, this approach concerns the variation of clustering properties of galaxy groups and clusters with their richness. Although such studies have been made for various cases (like comparison of the correlation functions between galaxies and clusters, or between clusters of different richness classes), the analysis presented here deals with it in a more systematic and synthetic way.

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