Computing three-point correlation function randoms counts without the randoms catalogue. (14th May 2019)

• Record Type: Journal Article
• Authors: Pearson, David W; Samushia, Lado
• Is Part Of: Monthly notices of the Royal Astronomical Society. Volume 486:Number 1(2019)
• Page Start: L105
• Page End: L109
• Publication Date: 2019-05-14
• Subjects: methods: numerical -- cosmology: miscellaneous -- large-scale structure of Universe; Astronomy -- Research -- Periodicals; Periodicals; 520.5
• DOI: 10.1093/mnrasl/slz067
• Languages: English
• ISSNs: 1745-3933

Abstract

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 $\mathcal {O}(N^2\log N)$ 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.