The ergodicity bias in the observed galaxy distribution
  The spatial distribution of galaxies we observed is subject to the given
condition that we, human beings are sitting right in a galaxy -- the Milky Way.
Thus the ergodicity assumption is questionable in interpretation of the
observed galaxy distribution. The resultant difference between observed
statistics (volume average) and the true cosmic value (ensemble average) is
termed as the ergodicity bias. We perform explicit numerical investigation of
the effect for a set of galaxy survey depths and near-end distance cuts. It is
found that the ergodicity bias in observed two- and three-point correlation
functions in most cases is insignificant for modern analysis of samples from
galaxy surveys and thus close a loophole in precision cosmology. However, it
may become non-negligible in certain circumstances, such as those applications
involving three-point correlation function at large scales of local galaxy
samples. Thus one is reminded to take extra care in galaxy sample construction
and interpretation of the statistics of the sample, especially when the
characteristic redshift is low.
