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...

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...