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 , \sim 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 [ \sim 30 , \sim 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 can not 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 .