Related papers: Accelerating the 2-point and 3-point galaxy correl…
The anisotropic 2-point correlation function (2PCF) of galaxies measures pairwise clustering as a function of the pair separation's angle to the line of sight. The latter is often defined as either the angle bisector of the…
Conventional estimators of the anisotropic power spectrum and two-point correlation function (2PCF) adopt the `Yamamoto approximation', fixing the line-of-sight of a pair of galaxies to that of just one of its members. Whilst this is…
The 3-Point Correlation Function (3PCF), which measures correlations between triplets of galaxies encodes information about peculiar velocities, which distort the observed positions of galaxies along the line of sight away from their true…
Measurements of line-of-sight dependent clustering via the galaxy power spectrum's multipole moments constitute a powerful tool for testing theoretical models in large-scale structure. Recent work shows that this measurement, including a…
We present an optimised multipole algorithm for computing the three-point correlation function (3PCF), tailored for application to large-scale cosmological datasets. The algorithm builds on a $in\, situ$ interpretation of correlation…
We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as $N^2$, with $N$ the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with…
We present an algorithm that computes the multipole coefficients of the galaxy three-point correlation function (3PCF) without explicitly considering triplets of galaxies. Rather, centering on each galaxy in the survey, it expands the…
We present a new $\texttt{python}$ package SARABANDE for measuring 3 & 4 Point Correlation Functions (3/4 PCFs) in $\mathcal{O}(N_{\rm g} \log N_{\rm g})$ time using Fast Fourier Transforms (FFTs), with $N_{\rm g}$ the number of grid points…
We study two key issues militating against the use of the anisotropic three-point correlation function (3PCF) for cosmological parameter inference: difficulties with its computational estimation and high-dimensionality. We show how…
We present a new algorithm to rapidly compute the two-point (2PCF), three-point (3PCF) and n-point (n-PCF) correlation functions in roughly O(N log N) time for N particles, instead of O(N^n) as required by brute force approaches. The…
The usual fluid equations describing the large-scale evolution of mass density in the universe can be written as local in the density, velocity divergence, and velocity potential fields. As a result, the perturbative expansion in small…
In the forthcoming large volume galaxy surveys higher order statistics will provide complementary information to the usual two point statistics. Low variance estimators of the Three Point Correlation Function (3CPF) of discrete data count…
Two-point correlation functions (2PCF) are widely used to characterize how points cluster in space. In this work, we study the problem of measuring the 2PCF over a large set of points, restricted to a subset satisfying a property of…
The nature of dark energy and the complete theory of gravity are two central questions currently facing cosmology. A vital tool for addressing them is the 3-point correlation function (3PCF), which probes deviations from a spatially random…
Ongoing and future spectroscopic galaxy surveys will cover unprecedented volumes with a number of objects large enough to effectively probe clustering anisotropies through higher-order statistics. In this work, we present a novel and…
N-Point Correlation Functions, usually with N = 2, 3, and their Fourier-space analogs power spectrum and bispectrum, are major tools used in cosmology to capture the clustering of large-scale structure. We outline how the clustering these…
The three-point correlation function (3PCF) can now be measured in large galaxy redshift surveys, but in three dimensions its interpretation is complicated by the presence of redshift-space distortions. I investigate the projected 3PCF,…
We establish a practical method for the joint analysis of anisotropic galaxy two- and three-point correlation functions (2PCF and 3PCF) on the basis of the decomposition formalism of the 3PCF using tri-polar spherical harmonics. We perform…
Efficient estimators of Fourier-space statistics for large number of objects rely on Fast Fourier Transforms (FFTs), which are affected by aliasing from unresolved small scale modes due to the finite FFT grid. Aliasing takes the form of a…
Ptychography is a popular imaging technique that combines diffractive imaging with scanning microscopy. The technique consists of a coherent beam that is scanned across an object in a series of overlapping positions, leading to reliable and…