Efficient computation of Npoint 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 Npoint correlation function (NPCF) encodes the distribution of Ntuplets of points in space; estimation of the NPCF basis coefficients from a set of n particles scales as n^{N}. 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 n^{2} 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:

 Astrophysics  Instrumentation and Methods for Astrophysics;
 Physics  Applied Physics;
 Physics  Computational Physics;
 Physics  Data Analysis;
 Statistics and Probability
 EPrint:
 12 pages, 3 figures, accepted by PNAS. Code available at https://github.com/oliverphilcox/NPCFs.jl