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 non-trivial scaling behavior, which resembles 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.