Are the 2dFGRS superstructures a problem for hierarchical models?
  We introduce an objective method to assess the probability of finding extreme
events in the distribution of cold dark matter such as voids, overdensities or
very high mass haloes. Our approach uses an ensemble of N-body simulations of
the hierar- chical clustering of dark matter to find extreme structures. The
frequency of extreme events, in our case the cell or smoothing volume with the
highest count of cluster-mass dark matter haloes, is well described by a Gumbel
distribution. This distribution can then be used to forecast the probability of
finding even more extreme events, which would otherwise require a much larger
ensemble of simulations to quantify. We use our technique to assess the chance
of finding concentrations of massive clusters or super- clusters, like the two
found in the two-degree field galaxy redshift survey (2dFGRS), using a
counts-in-cells analysis. The Gumbel distribution gives an excellent descrip-
tion of the distribution of extreme cell counts across two large ensembles of
simulations covering different cosmologies, and also when measuring the
clustering in both real and redshift space. We find examples of structures like
those found in the 2dFGRS in the simulations. The chance of finding such
structures in a volume equal to that of the 2dFGRS is around 2%.
