We introduce and study two new concepts which are essential for the quantitative analysis of the statistical quality of the available galaxy samples. These are the dilution effect and the small scale fluctuations. We show that the various data that are considered as pointing to a homogenous...

We analyze subsamples of Abell and ACO cluster catalogs, in order to study the spatial properties of the large-scale matter distribution. The subsamples analyzed are estimated to be nearly complete and are the standard ones used in the correlation analysis by various authors. The statistical...

Models of structure formation in the universe postulate that matter distributions observed today in galaxy catalogs arise, through a complex non-linear dynamics, by gravitational evolution from a very uniform initial state. Dark matter plays the central role of providing the primordial density...

We study the properties of the growth probabilities for diffusion limited aggregation and the dielectric breakdown model in the steady state regime of the cylinder geometry. The results show a rather unambiguous picture with the following properties: The projection of the growth probability...

We study various aspects of the self-organized critical phenomena. A continuous-energy model is analyzed using a self-consistent effective medium method. We find that energy is homogeneously and isotropically distributed in space. We have calculated analytically the critical energy, which is...