Large SDSS quasar groups and their statistical significance
  We use a volume-limited sample of quasars in the Sloan Digital Sky Survey
(SDSS) DR7 quasar catalog to identify quasar groups and address their
statistical significance. This quasar sample has a uniform selection function
on the sky and nearly a maximum possible contiguous volume that can be drawn
from the DR7 catalog. Quasar groups are identified by using the
Friend-of-Friend algorithm with a set of fixed comoving linking lengths. We
find that the richness distribution of the richest 100 quasar groups or the
size distribution of the largest 100 groups are statistically equivalent with
those of randomly-distributed points with the same number density and sky
coverage when groups are identified with the linking length of 70 h-1Mpc. It is
shown that the large-scale structures like the huge Large Quasar Group (U1.27)
reported by Clowes et al. (2013) can be found with high probability even if
quasars have no physical clustering, and does not challenge the initially
homogeneous cosmological models. Our results are statistically more reliable
than those of Nadathur (2013), where the test was made only for the largest
quasar group. It is shown that the linking length should be smaller than 50
h-1Mpc in order for the quasar groups identified in the DR7 catalog not to be
dominated by associations of quasars grouped by chance. We present 20 richest
quasar groups identified with the linking length of 70 h-1Mpc for further
analyses.
