  We discuss the estimation of galaxy correlation properties in several volume
limited samples, in different sky regions, obtained from the Fourth Data
Release of the Sloan Digital Sky Survey. The small scale properties are
characterized through the determination of the nearest neighbor probability
distribution. By using a very conservative statistical analysis, in the range
of scales [0.5,~30] Mpc/h we detect power-law correlations in the conditional
density in redshift space, with an exponent \gamma=1.0 \pm 0.1. This behavior
is stable in all different samples we considered thus it does not depend on
galaxy luminosity. In the range of scales [~30,~100] Mpc/h we find evidences
for systematic unaveraged fluctuations and we discuss in detail the problems
induced by finite volume effects on the determination of the conditional
density. We conclude that in such range of scales there is an evidence for a
smaller power-law index of the conditional density. However we cannot
distinguish between two possibilities: (i) that a crossover to homogeneity
(corresponding to \gamma=0 in the conditional density) occurs before 100 Mpc/h,
(ii) that correlations extend to scales of order 100 Mpc/h (with a smaller
exponent 0 < \gamma <1). We emphasize that galaxy distributions in these
samples present large fluctuations at the largest scales probed, corresponding
to the presence of large scale structures extending up to the boundaries of the
present survey. Finally we discuss several differences between the behavior of
the conditional density in mock galaxy catalogs built from cosmological N-body
simulations and real data. We discuss some theoretical implications of such a
fact considering also the super-homogeneous features of primordial density
fields.
