ConKer: evaluating isotropic correlations of arbitrary order

Abstract

High order correlations in the cosmic matter density have become increasingly valuable in cosmological analyses. However, computing such correlation functions is computationally expensive. We aim to circumvent these challenges by designing a new method of estimating correlation functions. This is realized in ConKer, an algorithm that performs FFT convolutions of matter distributions with spherical kernels. ConKer is applied to the CMASS sample of the SDSS DR12 galaxy survey and used to compute the isotropic correlation up to correlation order n = 5. We also compare the n = 2 and n = 3 cases to traditional algorithms to verify the accuracy of the new method. We perform a timing study of the algorithm and find that two of the three components of the algorithm are independent of the catalog size, N, while one component is O(N), which starts dominating for catalogs larger than 10M objects. For n < 5 the dominant calculation is O(N^(4/3logN)), where N is the number of the grid cells. For higher n, the execution time is expected to be dominated by a component with time complexity O(N^((n+2)/3)). We find ConKer to be a fast and accurate method of probing high order correlations in the cosmic matter density.

9 pages, 12 figures

References in corpus (5)

• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Observational systematics and baryon acoustic oscillations in the correlation function
• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: cosmological implications of the configuration-space clustering wedges
• An ideal mass assignment scheme for measuring the Power Spectrum with FFTs
• On the inadequacy of N-point correlation functions to describe nonlinear cosmological fields: explicit examples and connection to simulations
• ENCORE: An $\mathcal{O}(N_{\mathrm{g}}^2)$ Estimator for Galaxy $N$-Point Correlation Functions

Cited by in corpus (5)

• Bayesian deep learning for cosmic volumes with modified gravity
• Pair Counting without Binning -- A New Approach to Correlation Functions in Clustering Statistics
• Constraining primordial non-Gaussianity from the large scale structure two-point and three-point correlation functions
• Beyond the two-point correlation: constraining primordial non-gaussianity with density perturbation moments
• An Optimal In-Situ Multipole Algorithm for the Isotropic Three-Point Correlation Functions