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.
@article{arxiv.2108.01714,
title = {Analytic Gaussian Covariance Matrices for Galaxy $N$-Point Correlation Functions},
author = {Jiamin Hou and Robert N. Cahn and Oliver H. E. Philcox and Zachary Slepian},
journal= {arXiv preprint arXiv:2108.01714},
year = {2022}
}