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
  As deeper galaxy catalogues are soon to come, it becomes even more
importantto measure large-scale fluctuations in the catalogues with robust
statistics that cover all moments of the galaxy distribution.In this paper we
reinforce a direct analysis of galaxy data by employing the Germ-Grain method
to calculate thefamily of Minkowski Functionals. We introduce a new code,
suitable for the analysis of large data sets without smoothingand without the
construction of excursion sets. We provide new tools to measure correlation
properties, putting emphasis onexplicitly isolating non-Gaussian correlations
with the help of integral-geometric relations. As a first application we
present the analysis of large-scale fluctuations in the luminous red galaxy
sample of Sloan Digital Sky Survey data release 7 data. We findsignificant
deviations from the $\Lambda$ cold dark matter mock catalogues on samples as
large 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 these
deviations.
