Spatial density fluctuations and selection effects in galaxy redshift
  surveys
  One of the main problems of observational cosmology is to determine the range
in which a reliable measurement of galaxy correlations is possible. This
corresponds to determine the shape of the correlation function, its possible
evolution with redshift and the size and amplitude of large scale structures.
Different selection effects, inevitably entering in any observation, introduce
important constraints in the measurement of correlations. In the context of
galaxy redshift surveys selection effects can be caused by observational
techniques and strategies and by implicit assumptions used in the data
analysis. Generally all these effects are taken into account by using
pair-counting algorithms to measure two-point correlations. We review these
methods stressing that they are based on the a-priori assumption that galaxy
distribution is spatially homogeneous inside a given sample. We show that, when
this assumption is not satisfied by the data, results of the correlation
analysis are affected by finite size effects.In order to quantify these
effects, we introduce a new method based on the computation of the gradient of
galaxy counts along tiny cylinders. We show, by using artificial homogeneous
and inhomogeneous point distributions, that this method is to identify redshift
dependent selection effects and to disentangle them from the presence of large
scale density fluctuations. We then apply this new method to several redshift
catalogs and we find evidences that galaxy distribution, in those samples where
selection effects are small enough, is characterized by power-law correlations
with exponent $\gamma=0.9$ up to $20$ Mpc/h followed by a change of slope that,
in the range [20,100] Mpc/h, corresponds to a power-law exponent $\gamma=0.25$.
Whether a crossover to spatial unformity occurs at $\sim 100$ Mpc/h cannot be
clarified by the present data.
