scholarly journals Nearest neighbour distributions: New statistical measures for cosmological clustering

2020 ◽  
Vol 500 (4) ◽  
pp. 5479-5499 ◽  
Author(s):  
Arka Banerjee ◽  
Tom Abel
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Cosmological Parameters ◽  
Higher Order ◽  
Cumulative Distribution ◽  
Summary Statistics ◽  
Nearest Neighbour ◽  
Statistical Measures ◽  
Point Correlation ◽  
Point Correlation Function

ABSTRACT The use of summary statistics beyond the two-point correlation function to analyse the non-Gaussian clustering on small scales, and thereby, increasing the sensitivity to the underlying cosmological parameters, is an active field of research in cosmology. In this paper, we explore a set of new summary statistics – the k-Nearest Neighbour Cumulative Distribution Functions (kNN-CDF). This is the empirical cumulative distribution function of distances from a set of volume-filling, Poisson distributed random points to the k-nearest data points, and is sensitive to all connected N-point correlations in the data. The kNN-CDF can be used to measure counts in cell, void probability distributions, and higher N-point correlation functions, all using the same formalism exploiting fast searches with spatial tree data structures. We demonstrate how it can be computed efficiently from various data sets – both discrete points, and the generalization for continuous fields. We use data from a large suite of N-body simulations to explore the sensitivity of this new statistic to various cosmological parameters, compared to the two-point correlation function, while using the same range of scales. We demonstrate that the use of kNN-CDF improves the constraints on the cosmological parameters by more than a factor of 2 when applied to the clustering of dark matter in the range of scales between 10 and $40\, h^{-1}\, {\rm Mpc}$. We also show that relative improvement is even greater when applied on the same scales to the clustering of haloes in the simulations at a fixed number density, both in real space, as well as in redshift space. Since the kNN-CDF are sensitive to all higher order connected correlation functions in the data, the gains over traditional two-point analyses are expected to grow as progressively smaller scales are included in the analysis of cosmological data, provided the higher order correlation functions are sensitive to cosmology on the scales of interest.

scholarly journals Testing the efficiency of estimators of the two-point correlation function

2019 ◽  
Author(s):  
Lucas Bertoncello de Oliveira ◽  
Flavia Sobreira Sanchez
Keyword(s):  
Correlation Function ◽  
Dark Energy ◽  
Energy Density ◽  
Correlation Functions ◽  
Cosmological Parameters ◽  
Precision Measurements ◽  
Total Energy Density ◽  
Modern Cosmology ◽  
Point Correlation ◽  
Point Correlation Function

Since the discovery of the Universe’s expansion in 1998, studying its cause has been one of the main interests in cosmology. Today the simplest model that describes our Universe is known as LCDM where dark energy dominates 70% of the Universe’s total energy density. The discovery of 1998 motivated great advances in technology and the construction of telescopes, enabling modern cosmology to reach a “era of precision measurements”. Studying the distribution of galaxies in the observed Universe is a powerful tool to understanding our Universe’s dynamics and correlation functions have long since been used to study these distributions. In this project I study concepts of modern cosmology and statistics in order to be introduced to the two-point correlation function estimated from a catalog of galaxies to test cosmological models, such as the LCDM. The first part of this study was to compare different estimators of the two-point correlation function. In the second part, using the measurements of the first part, I will constrain cosmological parameters that dictate the dynamics of our Universe.

scholarly journals From correlation functions to event shapes in QCD

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
D. Chicherin ◽  
J. M. Henn ◽  
E. Sokatchev ◽  
K. Yan
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Event Shape ◽  
Proof Of Concept ◽  
Yang Mills ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Event Shapes ◽  
A Charge ◽  
Conserved Currents

Abstract We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.

scholarly journals Measuring Galaxy Bias from the High-Order Correlation Functions

1999 ◽  
Vol 183 ◽  
pp. 229-234
Author(s):  
Y.P. Jing
Keyword(s):  
Correlation Functions ◽  
Cosmological Parameters ◽  
High Order ◽  
Density Parameter ◽  
Theoretical Argument ◽  
Important Conclusion ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Galaxy Bias

In this talk, I will show how to determine the biasing factor b from the high-order moments of galaxies. The determination is based on the analytical modeling of primordial peaks and virialized halos and is independent of the currently unknown density parameter Ω0 and other cosmological parameters. The observed high-oder moments of the APM galaxies require that the biasing factor b be very close to 1, i.e. the optical galaxies are an unbiased tracer of the underlying mass distribution (on quasilinear scale). The theoretical argument can be easily generalized to the three-point correlation function and the bispectrum both of which can used as further observational tests to the important conclusion of b ≈ 1 drawn from the high-order moments. Finally I present our preliminary results of the three-point correlation functions for the Las Campanas Redshift Survey.

scholarly journals CRITICAL BEHAVIOR IN THE ROTATING D-BRANES

1999 ◽  
Vol 14 (27) ◽  
pp. 1895-1907 ◽  
Author(s):  
RONG-GEN CAI ◽  
KWANG-SUP SOH
Keyword(s):  
Correlation Function ◽  
Critical Behavior ◽  
Critical Exponents ◽  
Correlation Functions ◽  
Scaling Laws ◽  
Canonical Ensemble ◽  
Stable Boundary ◽  
Conformal Fields ◽  
Point Correlation ◽  
Point Correlation Function

We investigate the critical behavior near the thermodynamically stable boundary for the rotating D3-, M5- and M2-branes. The static scaling laws are found to hold. The critical exponents characterizing the scaling behaviors of susceptibilities are the same and all equal 1/2 in all cases. Using the scaling laws related to the correlation functions, we predict the critical exponents of the two-point correlation function of the corresponding conformal fields. We find that the stable boundary is shifted in the different ensembles and there does not exist the stable boundary in the canonical ensemble for the rotating M2-branes.

scholarly journals ON THE CONSTRUCTION OF CORRELATION FUNCTIONS FOR THE INTEGRABLE SUPERSYMMETRIC FERMION MODELS

2006 ◽  
Vol 20 (05) ◽  
pp. 505-549 ◽  
Author(s):  
SHAO-YOU ZHAO ◽  
WEN-LI YANG ◽  
YAO-ZHONG ZHANG
Keyword(s):  
Correlation Function ◽  
Physical Properties ◽  
Correlation Functions ◽  
Recent Progress ◽  
Integrable Models ◽  
Thermodynamical Limit ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Creation ◽  
Scalar Products

We review the recent progress on the construction of the determinant representations of the correlation functions for the integrable supersymmetric fermion models. The factorizing F-matrices (or the so-called F-basis) play an important role in the construction. In the F-basis, the creation (and the annihilation) operators and the Bethe states of the integrable models are given in completely symmetric forms. This leads to the determinant representations of the scalar products of the Bethe states for the models. Based on the scalar products, the determinant representations of the correlation functions may be obtained. As an example, in this review, we give the determinant representations of the two-point correlation function for the Uq(gl(2|1)) (i.e. q-deformed) supersymmetric t-J model. The determinant representations are useful for analyzing physical properties of the integrable models in the thermodynamical limit.

scholarly journals CORRELATION FUNCTIONS OF A CONFORMAL FIELD THEORY IN THREE DIMENSIONS

1996 ◽  
Vol 11 (13) ◽  
pp. 1047-1059 ◽  
Author(s):  
S. GURUSWAMY ◽  
P. VITALE
Keyword(s):  
Correlation Function ◽  
Power Law ◽  
Correlation Functions ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Radius Of Curvature ◽  
Nonlinear Sigma Model ◽  
Long Distance ◽  
Point Correlation ◽  
Point Correlation Function

We derive explicit forms of the two-point correlation functions of the O(N) nonlinear sigma model at the critical point, in the large-N limit, on various three-dimensional manifolds of constant curvature. The two-point correlation function, G(x, y), is the only n-point correlation function which survives in this limit. We analyze the short distance and long distance behaviors of G(x, y). It is shown that G(x, y) decays exponentially with the Riemannian distance on the spaces R2×S1, S1×S1×R, S2×R, H2×R. The decay on R3 is of course a power law. We show that the scale for the correlation length is given by the geometry of the space and therefore the long distance behavior of the critical correlation function is not necessarily a power law even though the manifold is of infinite extent in all directions; this is the case of the hyperbolic space where the radius of curvature plays the role of a scale parameter. We also verify that the scalar field in this theory is a primary field with weight [Formula: see text]; we illustrate this using the example of the manifold S2×R whose metric is conformally equivalent to that of R3–{0} up to a reparametrization.

scholarly journals Scale-Invariant Correlation Functions of Cosmological Density Fluctuations in the Strong Clustering Regime and the Stability

1999 ◽  
Vol 183 ◽  
pp. 274-274
Author(s):  
Taihei Yano ◽  
Naoteru Gouda
Keyword(s):  
Correlation Function ◽  
Spatial Correlation ◽  
Correlation Functions ◽  
Power Index ◽  
Nonlinear Regime ◽  
Peculiar Velocity ◽  
Strongly Nonlinear ◽  
Point Correlation ◽  
Point Correlation Function ◽  
The Mean

We have investigated the scale-invariant solutions of the BBGKY equations for spatial correlation functions of cosmological density fluctuations and the mean relative peculiar velocity in the strongly nonlinear regime. It is found that the solutions for the mean relative physical velocity depend on the three-point spatial correlation function and the skewness of the velocity fields. We find that the stable condition in which the mean relative physical velocity vanishes on the virialized regions is satisfied only under the assumptions which Davis & Peebles took in there paper. It is found, however, that their assumptions may not be general in real. The power index of the two-point correlation function in the strongly nonlinear regime depends on the mean relative peculiar velocity, the three-point correlation function and the skewness. If self-similar solutions exist, then the power index in the strongly nonlinear regime is related to the power index of the initial power spectrum and its relation depends on the three-point correlation function and the skewness through the mean relative peculiar velocity. We also investigate stability of the solutions of the BBGKY equations for two-point spatial correlation functions. In the case that the background skewness is equal to 0, we found that there is no local instability in the strongly non-linear regime.

scholarly journals Weak lensing cosmology with convolutional neural networks on noisy data

2019 ◽  
Vol 490 (2) ◽  
pp. 1843-1860 ◽  
Author(s):  
Dezső Ribli ◽  
Bálint Ármin Pataki ◽  
José Manuel Zorrilla Matilla ◽  
Daniel Hsu ◽  
Zoltán Haiman ◽  
...  
Keyword(s):  
Neural Networks ◽  
Correlation Function ◽  
Power Spectrum ◽  
Convolutional Neural Networks ◽  
Higher Order ◽  
Weak Lensing ◽  
Noise Levels ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Non Gaussian

ABSTRACT Weak gravitational lensing is one of the most promising cosmological probes of the late universe. Several large ongoing (DES, KiDS, HSC) and planned (LSST, Euclid, WFIRST) astronomical surveys attempt to collect even deeper and larger scale data on weak lensing. Due to gravitational collapse, the distribution of dark matter is non-Gaussian on small scales. However, observations are typically evaluated through the two-point correlation function of galaxy shear, which does not capture non-Gaussian features of the lensing maps. Previous studies attempted to extract non-Gaussian information from weak lensing observations through several higher order statistics such as the three-point correlation function, peak counts, or Minkowski functionals. Deep convolutional neural networks (CNN) emerged in the field of computer vision with tremendous success, and they offer a new and very promising framework to extract information from 2D or 3D astronomical data sets, confirmed by recent studies on weak lensing. We show that a CNN is able to yield significantly stricter constraints of (σ8, Ωm) cosmological parameters than the power spectrum using convergence maps generated by full N-body simulations and ray-tracing, at angular scales and shape noise levels relevant for future observations. In a scenario mimicking LSST or Euclid, the CNN yields 2.4–2.8 times smaller credible contours than the power spectrum, and 3.5–4.2 times smaller at noise levels corresponding to a deep space survey such as WFIRST. We also show that at shape noise levels achievable in future space surveys the CNN yields 1.4–2.1 times smaller contours than peak counts, a higher order statistic capable of extracting non-Gaussian information from weak lensing maps.

Study of the time evolution of correlation functions of the transverse Ising chain with ring frustration by perturbative theory

2018 ◽  
Vol 32 (10) ◽  
pp. 1850121
Author(s):  
Zhen-Yu Zheng ◽  
Peng Li
Keyword(s):  
Correlation Function ◽  
Schrödinger Equation ◽  
Time Evolution ◽  
Correlation Functions ◽  
Schrodinger Equation ◽  
Transverse Field ◽  
Time Dependent ◽  
Ising Chain ◽  
Point Correlation ◽  
Point Correlation Function

We consider the time evolution of two-point correlation function in the transverse-field Ising chain (TFIC) with ring frustration. The time-evolution procedure we investigated is equivalent to a quench process in which the system is initially prepared in a classical kink state and evolves according to the time-dependent Schrödinger equation. Within a framework of perturbative theory (PT) in the strong kink phase, the evolution of the correlation function is disclosed to demonstrate a qualitatively new behavior in contrast to the traditional case without ring frustration.

scholarly journals Massive neutrinos leave fingerprints on cosmic voids

2019 ◽  
Vol 488 (3) ◽  
pp. 4413-4426 ◽  
Author(s):  
Christina D Kreisch ◽  
Alice Pisani ◽  
Carmelita Carbone ◽  
Jia Liu ◽  
Adam J Hawken ◽  
...  
Keyword(s):  
Correlation Function ◽  
Cold Dark Matter ◽  
Opposite Effect ◽  
Cosmological Parameters ◽  
Neutrino Masses ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Massive Neutrinos ◽  
Cosmic Voids ◽  
Simulation Volume

ABSTRACT Do void statistics contain information beyond the tracer 2-point correlation function? Yes! As we vary the sum of the neutrino masses, we find void statistics contain information absent when using just tracer 2-point statistics. Massive neutrinos uniquely affect cosmic voids. We explore their impact on void clustering using both the DEMNUni and MassiveNuS simulations. For voids, neutrino effects depend on the observed void tracers. As the neutrino mass increases, the number of small voids traced by cold dark matter particles increases and the number of large voids decreases. Surprisingly, when massive, highly biased, haloes are used as tracers, we find the opposite effect. The scale at which voids cluster, as well as the void correlation, is similarly sensitive to the sum of neutrino masses and the tracers. This scale-dependent trend is not due to simulation volume or halo density. The interplay of these signatures in the void abundance and clustering leaves a distinct fingerprint that could be detected with observations and potentially help break degeneracies between different cosmological parameters. This paper paves the way to exploit cosmic voids in future surveys to constrain the mass of neutrinos.

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