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 the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) Γ(r) is a power law up to the sample effective depth (∼ 30 h−1 Mpc), showing the fractal nature of the galaxy distribution in this catalog. The...

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...

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...

The Hamiltonian of an elastic string pinned by random potentials is often used to describe the depinning transition of a charge density wave in the presence of impurity pinning. The properties of the pinned states show close analogies to those of glassy systems, while the depinning transition...

The distribution of first digits in numbers series obtained from very different origins shows a marked asymmetry in favor of small digits that goes under the name of Benford's law. We analyze in detail this property for different data sets and give a general explanation for the origin of the...

We present a detailed analysis of the self-organization phenomenon in which the stylized facts originate from finite size effects with respect to the number of agents considered and disappear in the limit of an infinite population. By introducing the possibility that agents can enter or leave...