We report the results of a statistical analysis of the space distribution of galaxies of the 2MRS catalog, which contains redshifts of 43533 galaxies of the 2MASS all-sky IR survey. Because of the unique features of the 2MRS survey, such as its 90% sky coverage, galaxy selection in the IR, the complete incorporation of the old stellar population of galaxies, weakness of the dust extinction effects, and the smallness of the k-and e-corrections allowed us to determine the statistical properties of the global distribution of galaxies in the Local Universe. We took into account the main methodological factors that distort the theoretically expected relations compared to those actually observed. We construct the radial galaxy number counts N (R), SL(R, r) statistics, and the complete correlation function (conditional density) Γ(r) for volume-limited (VL) galaxy samples. The observed conditional density Γ(r) in the redshift space is independent of the luminosity of galaxies and has the form of a power-law function with exponent γ ≈ 1.0 over a large range scale-length spanning from 0.1 to 100 Mpc. We compare the statistical properties of the space distribution of galaxies of the 2MRS catalog with the corresponding properties of simulated catalogs: stochastic fractal distributions and galaxies of the Millennium catalog.

Abstract. 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 γ = 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 γ = 0.25. Whether a crossover to spatial unformity occurs at ∼ 100 Mpc/h cannot be clarified by the present data.