Scale-invariant clustering in the large-scale distribution of galaxies

We explore the scaling properties of galaxy clustering through an analysis of the new redshift survey of the Perseus-Pisces region and of other published data. At small separations we measure the "standard" scaling, with the well-known correlation dimension D congruent-to 1.2 shown by the two-point correlation analyses. On larger scales, however, we evidence the existence of a second range with a different scaling characterized by a correlation dimension D congruent-to 2.2. Homogeneity seems to be reached for separations > 30h-1 Mpc. We discuss the possible implications of this result concerning the origin of structure. Interpreting the large-scale D approximately 2 range as due to fluctuations which are still in the linear regime, it provides evidence that the present structure could have developed from simple scale-free initial conditions characterized by a power spectrum \delta(k)\2 is-proportional-to k-2.