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Main Authors: Slepian, Zcahary, Greco, Alessandro
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.18547
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author Slepian, Zcahary
Greco, Alessandro
author_facet Slepian, Zcahary
Greco, Alessandro
contents Previous work (Slepian 2024) showed that the Smith-Zaldarriaga (2011) algorithm to realize Cosmic Microwave Background (CMB) maps with any desired harmonic-space bispectrum could be generalized to produce a 3D density field with any desired N-Point Correlation Functions (NPCFs, N = $2, 3, \ldots$) about a particular, specified set of ``primary'' points. This algorithm assured one of having the correct correlations if measured about these specific centers. Here, we show that this algorithm was more general than initially believed, and can in fact be used to produce a density field on a grid that has the correct, desired NPCFs as measured about \textit{every} point on the grid. This paper should be considered the second in the series, and now completes the quest to generalize the idea of ``constrained realization'' (Hoffman and Ribak 1991) to higher-order statistics. This algorithm will be of great use for quickly generating density fields both to produce covariance matrices, and test systematics, for current and future 3D large-scale structure surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, Spherex, and Roman.
format Preprint
id arxiv_https___arxiv_org_abs_2512_18547
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Harmony of the Spheres: Extension to All Points of an Algorithm for Producing a Density Field with Given Two-, Three-, and Four-Point Correlation Functions
Slepian, Zcahary
Greco, Alessandro
Cosmology and Nongalactic Astrophysics
Previous work (Slepian 2024) showed that the Smith-Zaldarriaga (2011) algorithm to realize Cosmic Microwave Background (CMB) maps with any desired harmonic-space bispectrum could be generalized to produce a 3D density field with any desired N-Point Correlation Functions (NPCFs, N = $2, 3, \ldots$) about a particular, specified set of ``primary'' points. This algorithm assured one of having the correct correlations if measured about these specific centers. Here, we show that this algorithm was more general than initially believed, and can in fact be used to produce a density field on a grid that has the correct, desired NPCFs as measured about \textit{every} point on the grid. This paper should be considered the second in the series, and now completes the quest to generalize the idea of ``constrained realization'' (Hoffman and Ribak 1991) to higher-order statistics. This algorithm will be of great use for quickly generating density fields both to produce covariance matrices, and test systematics, for current and future 3D large-scale structure surveys such as Dark Energy Spectroscopic Instrument (DESI), Euclid, Spherex, and Roman.
title Harmony of the Spheres: Extension to All Points of an Algorithm for Producing a Density Field with Given Two-, Three-, and Four-Point Correlation Functions
topic Cosmology and Nongalactic Astrophysics
url https://arxiv.org/abs/2512.18547