Galaxy redshift surveys represent one of the cornerstones of modern cosmology. In the past decades we have assisted to an exponential growth of the data, which have revealed that galaxies are organized in a large-scale network of filaments and voids. Statistical analysis of these surveys have shown that these structures correspond to power-law correlations.

Correspondingly, the density fluctuations follow the Gumbel distribution of extreme value statistics that is clearly distinguishable from a Gaussian distribution, which would arise in case of a homogeneous galaxy spatial configuration. A Gumbel distribution decays slower than a Gaussian, implying that large fluctuations are more probable than for a Gaussian process. There are thus important similarities between the galaxy distribution and critical systems of statistical physics, at least of scales smaller than 100 Mpc.

Below there is a reconstruction of the three dimensional fluctuation field in the SDSS survey. A larger scale structure, the Great Wall in this case, appears as a mountain chain, i.e a spatially extended structure.

Whether or not, on larger scales, correlations decay and the distribution crossovers to uniformity, is still matter of considerable debate. The principal questions concern indeed the nature of galaxy structures, the type of correlations and their spatial extension and the statistical properties of fluctuations distribution. The clarification of these points is crucial for the testing of cosmological models of structure formation. There is indeed a intense debate in the field stimulated by our results. For instance **Steven Weinberg** in his book “Cosmology” (2008) Oxford University, at pg.1 (first sentence) writes

##### *The visible universe seems the same in all directions around us, at least if we look out to distances larger than about 300 million light years. (see K. K. S.Wu, O. Lahav, and M. J. Rees, Nature 397, 225 (January 21, 1999). For a contrary view, see P. H. Coleman, L. Pietronero, and R. H. Sanders, Astron. Astrophys. 200, L32 (1988): L. Pietronero, M. Montuori, and F. Sylos-Labini, in Critical Dialogues in Cosmology, (World Scientific, Singapore, 1997): 24; F. Sylos-Labini, F. Montuori, and L. Pietronero, Phys. Rep. 293, 61 (1998)).*

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