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Galaxy distribution and extreme value statistics

We consider the conditional galaxy density around each galaxy, and study its fluctuations in the newest samples of the Sloan Digital Sky Survey Data Release 7. Over a large range of scales, both the average conditional density and its variance show a nontrivial scaling behavior, which resembles to criticality. The density depends, for 10 < r < 80 Mpc/h, only weakly (logarithmically) on the system size. Correspondingly, we find that the density fluctuations follow the Gumbel distribution of extreme value statistics. This distribution is clearly distinguishable from a Gaussian distribution, which would arise for a homogeneous spatial galaxy configuration. We also point out similarities between the galaxy distribution and critical systems of statistical physics.