Efficient computation of N-point correlation functions in D dimensions
Abstract
Stochastic processes appear throughout the physical sciences, and their properties are usually described by correlation functions. For discrete data, the N-point correlation function (NPCF) encodes the distribution of N-tuplets of points in space; estimation of the NPCF basis coefficients from a set of n particles scales as nN. As N increases, this measurement becomes prohibitively expensive; thus, statistics with N > 3 are rarely used. Here, we show that NPCF components may be estimated in n2 time, by first expanding the statistics in separable angular bases. This approach has already found substantial application in quantifying galaxy clustering; here, we show it to be applicable to any homogeneous and isotropic space, regardless of dimension, and provide a practical implementation in Julia.
- Publication:
-
Proceedings of the National Academy of Science
- Pub Date:
- August 2022
- DOI:
- 10.1073/pnas.2111366119
- arXiv:
- arXiv:2106.10278
- Bibcode:
- 2022PNAS..11911366P
- Keywords:
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- Astrophysics - Instrumentation and Methods for Astrophysics;
- Physics - Applied Physics;
- Physics - Computational Physics;
- Physics - Data Analysis;
- Statistics and Probability
- E-Print:
- 12 pages, 3 figures, accepted by PNAS. Code available at https://github.com/oliverphilcox/NPCFs.jl