Computing three-point correlation function randoms counts without the randoms catalogue
Abstract
As we move towards future galaxy surveys, the three-point statistics will be increasingly leveraged to enhance the constraining power of the data on cosmological parameters. An essential part of the three-point function estimation is performing triplet counts of synthetic data points in random catalogues. Since triplet counting algorithms scale at best as O(N^2 log N) with the number of particles and the random catalogues are typically at least 50 times denser than the data; this tends to be by far the most time-consuming part of the measurements. Here, we present a simple method of computing the necessary triplet counts involving uniform random distributions through simple one-dimensional integrals. The method speeds up the computation of the three-point function by orders of magnitude, eliminating the need for random catalogues, with the simultaneous pair and triplet counting of the data points alone being sufficient.
- Publication:
-
Monthly Notices of the Royal Astronomical Society
- Pub Date:
- June 2019
- DOI:
- 10.1093/mnrasl/slz067
- arXiv:
- arXiv:1903.09715
- Bibcode:
- 2019MNRAS.486L.105P
- Keywords:
-
- methods: numerical;
- cosmology: miscellaneous;
- large-scale structure of Universe;
- Astrophysics - Cosmology and Nongalactic Astrophysics
- E-Print:
- Accepted to MNRAS Letters