Related papers: A comparison of estimators for the two-point corre…
The pair correlation function is a fundamental spatial point process characteristic that, given the intensity function, determines second order moments of the point process. Non-parametric estimation of the pair correlation function is a…
We present two related techniques to measure the two-point correlation function and the power spectrum with edge correction in any spatial dimensions. The underlying algorithm uses fast Fourier transforms for calculating the two-point…
While all the cosmological observations are carried out on a light-cone, the null hypersurface of an observer at z=0, the clustering statistics has been properly defined only on the constant-time hypersurface. We develop a theoretical…
Direct measurements of Hubble parameters $H(z)$ are very useful for cosmological model parameters inference. Based on them, Sahni, Shafieloo and Starobinski introduced a two-point diagnostic $Omh^2(z_i, z_j)$ as an interesting tool for…
The standard estimator for the two-point function of a homogeneous and isotropic random field is a special case of a larger class of least squares estimators that interpolate the function values. Using a different interpolation scheme,…
We present an analysis of the two-point peculiar velocity correlation function using data from the CosmicFlows catalogues. The Millennium and MultiDark Planck 2 N-body simulations are used to estimate cosmic variance and uncertainties due…
The existence of noncompatible observables in quantum theory makes a direct operational interpretation of two-point correlation functions problematic. Here we challenge such a view by explicitly constructing a measuring scheme that,…
An accurate fitting formula is reported for the two-point correlation function of the dark matter halos in hierarchical clustering models, It is valid for the the linearly clustering regime, and its accuracy is about 10% in the correlation…
We present a comparative study of the accuracy and precision of correlation function methods and full-field inference in cosmological data analysis. To do so, we examine a Bayesian hierarchical model that predicts log-normal fields and…
The fully general calculation of the cosmic error on N-point correlation functions and related quantities is presented. More precisely, the variance caused by the finite volume, discreteness, and edge effects is determined for {\em any}…
We introduce new estimators of the inhomogeneous $K$-function and the pair correlation function of a spatial point process as well as the cross $K$-function and the cross pair correlation function of a bivariate spatial point process under…
The two-point correlation function is computed for galaxies and groups of galaxies selected using 3-dimensional information from the Updated Zwicky Galaxy Catalog - (UZC). The redshift space distortion of the correlation function…
We present a method for fast evaluation of the covariance matrix for a two-point galaxy correlation function (2PCF) measured with the Landy-Szalay estimator. The standard way of evaluating the covariance matrix consists in running the…
Maximising the information that can be extracted from weak lensing measurements is a key goal for upcoming surveys such as LSST and Euclid. This is typically achieved through statistics that are complementary to the cosmic shear two-point…
We investigate to which accuracy it is possible to recover the real-space two-point correlation function of galaxy clusters from cluster catalogues based on photometric redshifts, and test our ability to measure the redshift and mass…
Distance correlation is a novel class of multivariate dependence measure, taking positive values between 0 and 1, and applicable to random vectors of arbitrary dimensions, not necessarily equal. It offers several advantages over the…
We use the formalism of Szapudi(2004} to derive full explicit expressions for the linear two-point correlation function, including redshift space distortions and large angle effects. We take into account a non-perturbative geometric term in…
We consider a situation where the density and peculiar velocities in real space are linear, and we calculate \xi_s the two-point correlation function in redshift space, incorporating all non-linear effects which arise as a consequence of…
Data from the ongoing \textit{Euclid} survey will map out billions of galaxies in the Universe, covering more than a third of the sky. This data will provide a wealth of information about the large-scale structure (LSS) of the Universe and…
Context: Two-point correlation functions are used throughout cosmology as a measure for the statistics of random fields. When used in Bayesian parameter estimation, their likelihood function is usually replaced by a Gaussian approximation.…