Statistical properties of galaxy distributions

The recent availability of complete three dimensional samples of galaxies and clusters permits a direct study of their spatial properties. We present a brief review of galaxy correlations based on the methods modern statistical Physics. These methods which able to identify self-similar and non-analytical prop ties, allow us to test the usual homogeneity assumption of luminous matter distribution. We conclude that both the three dimensional prop ties, and the angular log N - log S relation, point out the fact that the distribution of galaxies and clusters fractal with D ≈ 2 up to the deepest scale probed luminous matter (≈≥ 1000h-1 Mpc). This result has important implications for the theoretical framework that should be adopted