Estimating N-Point Correlation Functions from Pixelized Sky Maps

Abstract

We develop, implement and test a set of algorithms for estimating N-point correlation functions from pixelized sky maps. These algorithms are slow, in the sense that they do not break the O(N_pix^N) barrier, and yet, they are fast enough for efficient analysis of data sets up to several hundred thousand pixels. The typical application of these methods is Monte Carlo analysis using several thousand realizations, and therefore we organize our programs so that the initialization cost is paid only once. The effective cost is then reduced to a few additions per pixel multiplet (pair, triplet etc.). Further, the algorithms waste no CPU time on computing undesired geometric configurations, and, finally, the computations are naturally divided into independent parts, allowing for trivial (i.e., optimal) parallelization.

11 pages, 8 figures, accepted for publication in ApJS; textual improvements, references updated

References in corpus (13)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Preliminary Maps and Basic Results
• The Three--Point Correlation Function of the Cosmic Microwave Background in Inflationary Models
• Three-Point Correlations in Weak Lensing Surveys: Model Predictions and Applications
• The APM Galaxy Survey III: An Analysis of Systematic Errors in the Angular Correlation Function and Cosmological Implications
• Tests for Non-Gaussian Statistics in the DMR Four-Year Sky Maps
• The Angular Correlation Function of Galaxies from Early SDSS Data
• The Three-point Correlation Function of Galaxies Determined from the Las Campanas Redshift Survey
• The Two-Point Correlation Function of Rich Clusters of Galaxies: Results from an Extended APM Cluster Redshift Survey
• The Projected Three-point Correlation Function: Theory and Observations
• The 3-point function in the large scale structure: I. The weakly non-linear regime in N-body simulations
• The APM cluster-galaxy cross-correlation function : Constraints on Omega and galaxy bias
• Patterns in the weak shear 3-point correlation function
• The N-point correlation functions of the COBE-DMR maps revisited

Cited by in corpus (9)

• Planck 2013 results. XXIII. Isotropy and statistics of the CMB
• Modeling the angular correlation function and its full covariance in Photometric Galaxy Surveys
• The N-point correlation functions of the first-year Wilkinson Microwave Anisotropy Probe sky maps
• What is the best way to measure baryonic acoustic oscillations?
• Clustering of photometric luminous red galaxies I : Growth of Structure and Baryon Acoustic Feature
• The effects of halo alignment and shape on the clustering of galaxies
• Fast Calculation of the Weak Lensing Aperture Mass Statistic
• Detecting unresolved moving sources in a diffuse background
• The two-and three-point correlation functions of the polarized five-year WMAP sky maps