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As deeper galaxy catalogues are soon to come, it becomes even moreimportantto measure large-scale fluctuations in the catalogues with robuststatistics that cover all moments of the galaxy distribution.In this paper wereinforce a direct analysis of galaxy data by employing the Germ-Grain methodto calculate thefamily of Minkowski Functionals. We introduce a new code,suitable for the analysis of large data sets without smoothingand without theconstruction of excursion sets. We provide new tools to measure correlationproperties, putting emphasis onexplicitly isolating non-Gaussian correlationswith the help of integral-geometric relations. As a first application wepresent the analysis of large-scale fluctuations in the luminous red galaxysample of Sloan Digital Sky Survey data release 7 data. We findsignificantdeviations from the $\Lambda$ cold dark matter mock catalogues on samples aslarge as $500h^{-1}$Mpc (more than $3\sigma$)and slight deviations of around$2\sigma$ on $700h^{-1}$Mpc, and we investigate possible sources of thesedeviations.

monthly notices of the royal astronomical society

Direct Minkowski Functional analysis of large redshift surveys: a new  high--speed code tested on the luminous red galaxy Sloan Digital Sky  Survey-DR7 catalogue