Computing three-point correlation function randoms counts without the randoms catalogue

Journal Article · 13 May 2019 · Monthly Notices of the Royal Astronomical Society: Letters

DOI: https://doi.org/10.1093/mnrasl/slz067 · OSTI ID:1515796

Pearson, David W. ^[1]; Samushia, Lado ^[2]

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1. Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA
2. Department of Physics, Kansas State University, 116 Cardwell Hall, Manhattan, KS 66506, USA, National Abastumani Astrophysical Observatory, Ilia State University, 2A Kazbegi Ave., GE-1060 Tbilisi, Georgia

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.

• Research Organization: Kansas State Univ., Manhattan, KS (United States)
• Sponsoring Organization: National Aeronautics and Space Administration (NASA); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: SC0011840
• OSTI ID: 1515796
• Journal Information: Monthly Notices of the Royal Astronomical Society: Letters, Journal Name: Monthly Notices of the Royal Astronomical Society: Letters Journal Issue: 1 Vol. 486; ISSN 1745-3925
• Publisher: Royal Astronomical SocietyCopyright Statement
• Country of Publication: United Kingdom
• Language: English