Improved two-point correlation function estimates using glass-like
  distributions as a reference sample
  All estimators of the two-point correlation function are based on a random
catalogue, a set of points with no intrinsic clustering following the selection
function of a survey. High-accuracy estimates require the use of large random
catalogues, which imply a high computational cost. We propose to replace the
standard random catalogues by glass-like point distributions or glass
catalogues, which are characterized by a power spectrum $P(k)\propto k^4$ and
exhibit significantly less power than a Poisson distribution with the same
number of points on scales larger than the mean inter-particle separation. We
show that these distributions can be obtained by iteratively applying the
technique of Zeldovich reconstruction commonly used in studies of baryon
acoustic oscillations (BAO). We provide a modified version of the widely used
Landy-Szalay estimator of the correlation function adapted to the use of glass
catalogues and compare its performance with the results obtained using random
samples. Our results show that glass-like samples do not add any bias with
respect to the results obtained using Poisson distributions. On scales larger
than the mean inter-particle separation of the glass catalogues, the modified
estimator leads to a significant reduction of the variance of the Legendre
multipoles $\xi_\ell(s)$ with respect to the standard Landy-Szalay results with
the same number of points. The size of the glass catalogue required to achieve
a given accuracy in the correlation function is significantly smaller than when
using random samples. Even considering the small additional cost of
constructing the glass catalogues, their use could help to drastically reduce
the computational cost of configuration-space clustering analysis of future
surveys while maintaining high-accuracy requirements.
