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Analytic Gaussian Covariance Matrices for Galaxy $N$-Point Correlation Functions
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abstract
We derive analytic covariance matrices for the $N$-Point Correlation Functions (NPCFs) of galaxies in the Gaussian limit. Our results are given for arbitrary $N$ and projected onto the isotropic basis functions of Cahn & Slepian (2020), recently shown to facilitate efficient NPCF estimation. A numerical implementation of the 4PCF covariance is compared to the sample covariance obtained from a set of lognormal simulations, Quijote dark matter halo catalogues, and MultiDark-Patchy galaxy mocks, with the latter including realistic survey geometry. The analytic formalism gives reasonable predictions for the covariances estimated from mock simulations with a periodic-box geometry. Furthermore, fitting for an effective volume and number density by maximizing a likelihood based on Kullback-Leibler divergence is shown to partially compensate for the effects of a non-uniform window function.
Forward citations
Cited by 4 Pith papers
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Testing parity with composite-field spectra of BOSS and DESI luminous red galaxies
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No evidence for parity violation in BOSS
New statistics applied to BOSS data show the reported parity violation signal is consistent with zero after accounting for eight-point correlation function mismatch between data and mocks.
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Parity-odd Four-Point Correlation Function from DESI Data Release 1 Luminous Red Galaxy Sample
The parity-odd four-point correlation function measured in DESI DR1 LRGs is consistent with zero after correcting for survey-induced covariance mismatches.
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Measurement of Parity-Violating Modes of the Dark Energy Spectroscopic Instrument (DESI) Year 1 Luminous Red Galaxies' 4-Point Correlation Function
DESI's first parity-violation search shows a strong auto-correlation signal that disappears when the sky is split into patches, pointing to underestimated mocks' variance rather than new physics.
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