STATISTICAL PROPERTIES OF GALAXY CLUSTER DISTRIBUTION

We analyze subsamples of Abell and ACO cluster catalogs, in order to s tudy the spatial properties of the large-scale matter distribution. Th e subsamples analyzed are estimated to be nearly complete and are the standard ones used in the correlation analysis by various authors. The statistical analysis of cluster correlations is performed without any assumptions on the nature of the distribution itself. The cluster sam ples show fractal correlations up to sample limits (approximate to 70 h(-1) Mpc) with fractal dimension D approximate to 2, without any tend ency towards homogenization. Our analysis shows that the standard corr elation methods are incorrect, since they give a finite correlation le ngth for a distribution that does not possess one. In particular, the so-called correlation length r(0) is shown to be simply a fraction of the sample size. Moreover we conclude that galaxies and clusters are t wo different representations of the same self-similar structure and th at the correlations of clusters are the continuation of those of galax ies to larger scales.