Related papers: Cosmic Statistics of Statistics: N-point Correlati…
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…
This paper focuses on two aspects of the statistics of cosmological observables that are important for the next stages of precision cosmology. First, we note that the theory of reduced angular $N$-point spectra has only been developed in…
The fluctuations in the cosmic microwave background radiation may contain deviations from gaussian statistics which would be reflected in a nonzero value of three-point correlation function of $\Delta T$. However, any potential observation…
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…
We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…
We examine the errors on counts in cells extracted from galaxy surveys. The measurement error, related to the finite number of sampling cells, is disentangled from the ``cosmic error'', due to the finiteness of the survey. Using the…
Cosmological observables rely heavily on summary statistics such as two-point correlation functions. In many practical cases (e.g. the weak-lensing cosmic shear), those correlation functions are estimated from a finite, discrete sample of…
The relation between the results of cosmological N-body simulations, and the continuum theoretical models they simulate, is currently not understood in a way which allows a quantification of N dependent effects. In this first of a series of…
We calculate the lowest-order non-linear contributions to the power spectrum, two-point correlation function, and smoothed variance of the density field, for Gaussian initial conditions and scale-free initial power spectra, $P(k) \sim k^n$.…
Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap…
In order to quantify the error budget in the measured probability distribution functions of cell densities, the two-point statistics of cosmic densities in concentric spheres is investigated. Bias functions are introduced as the ratio of…
We present here a new algorithm for the fast computation of N-point correlation functions in large astronomical data sets. The algorithm is based on kdtrees which are decorated with cached sufficient statistics thus allowing for orders of…
A class of improved estimators is proposed for N-point correlation functions of galaxy clustering, and for discrete spatial random processes in general. In the limit of weak clustering, the variance of the unbiased estimator converges to…
The success of present and future cosmological studies is tied to the ability to detect discrepancies in complex data sets within the framework of a cosmological model. Tensions caused by the presence of unknown systematic effects need to…
Correlation functions and related statistics have been favorite measures of the distributions of extragalactic objects ever since people started analyzing the clustering of the galaxies in the 1930s. I review the evolving reasons for this…
The shapes of galaxy N-point correlation functions can be used as standard rulers to constrain the distance-redshift relationship and thence the expansion rate of the Universe. The cosmological density fields traced by late-time galaxy…
Cosmological weak lensing is the powerful probe of cosmology. Here we address one of the most fundamental, statistical questions inherent in weak lensing cosmology: whether or not we can recover the initial Gaussian information content of…
Connected $N$-point amplitudes in quantum field theory are enhanced by a factor of $N!$ in appropriate regimes of kinematics and couplings, but the non-perturbative analysis of this for collider physics applications is subtle. We resolve…
We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry…
We study the asymmetry in the two-point cross-correlation function of two populations of galaxies focusing in particular on the relativistic effects that include the gravitational redshift. We derive the cross-correlation function on small…