Spatial and Luminosity Properties of the Perseus-Pisces Redshift Survey

We analyze the spatial and the luminosity properties of the Perseus-Pisces redshift survey. We find that the two point correlation function (CF) $\Gamma(r)$ is a power law up to the sample effective depth ($\sim 30 h^{-1}Mpc$), showing the fractal nature of the galaxy distribution in this catalog. The fractal dimension turns out to be $D \approx 2$. We also consider the CF $\xi(r)$ and in particular the behavior of the "{\it correlation length}" $r_0$ ($\xi(r_{0})\equiv 1$) as function of the sample size. In this respect we find, unambiguously, that the luminosity segregation effect is not supported by any experimental evidence. In addition we have studied the galaxian number-density ($n(r)$) and number-counts ($N(m)$) in the VL subsamples finding a good agreement with the properties of a fractal distribution. In particular our conclusion is that the $n(r)$ relation allows to extend the analysis of the fractal nature up to a deeper depth than that reached by the CF analysis, and, we find evidence for fractal properties up to the limiting depth of $120-140 h^{-1} Mpc$. We stress that the $N(m)$ relation must be studied in VL subsamples rather than in magnitude limited ones as usually done. Finally we have considered the correlations between galaxy positions and luminosities by means of the multifractal analysis. We find clear evidence for self-similar behavior of the whole luminosity-space distribution. These results confirm and extend those of Coleman \& Pietronero (1992).