Point Correlation Function Research Articles

Crystallization of deformed Virasoro algebra, Ding-Iohara-Miki algebra, and 5D AGT correspondence

In this paper, we consider the q→0 limit of the deformed Virasoro algebra and that of the level 1, 2 representation of the Ding-Iohara-Miki algebra. Moreover, 5D AGT correspondence in this limit is discussed. This specialization corresponds to the limit from Macdonalds functions to Hall-Littlewood functions. Using the theory of Hall-Littlewood functions, some problems are solved. For example, the simplest case of 5D AGT conjectures is proven in this limit, and we obtain a formula for the 4-point correlation function of a certain operator.

Statistical representative elementary volumes of porous media determined using greyscale analysis of 3D tomograms

Digital rock physics carries the dogmatic concept of having to segment volume images for quantitative analysis but segmentation rejects huge amounts of signal information. Information that is essential for the analysis of difficult and marginally resolved samples, such as materials with very small features, is lost during segmentation. In X-ray nanotomography reconstructions of Hod chalk we observed partial volume voxels with an abundance that limits segmentation based analysis. Therefore, we investigated the suitability of greyscale analysis for establishing statistical representative elementary volumes (sREV) for the important petrophysical parameters of this type of chalk, namely porosity, specific surface area and diffusive tortuosity, by using volume images without segmenting the datasets. Instead, grey level intensities were transformed to a voxel level porosity estimate using a Gaussian mixture model. A simple model assumption was made that allowed formulating a two point correlation function for surface area estimates using Bayes’ theory. The same assumption enables random walk simulations in the presence of severe partial volume effects. The established sREVs illustrate that in compacted chalk, these simulations cannot be performed in binary representations without increasing the resolution of the imaging system to a point where the spatial restrictions of the represented sample volume render the precision of the measurement unacceptable. We illustrate this by analyzing the origins of variance in the quantitative analysis of volume images, i.e. resolution dependence and intersample and intrasample variance. Although we cannot make any claims on the accuracy of the approach, eliminating the segmentation step from the analysis enables comparative studies with higher precision and repeatability.

Stable clustering and the resolution of dissipationless cosmological N-body simulations

The determination of the resolution of cosmological N-body simulations, i.e., the range of scales in which quantities measured in them represent accurately the continuum limit, is an important open question. We address it here using scale-free models, for which self-similarity provides a powerful tool to control resolution. Such models also provide a robust testing ground for the so-called stable clustering approximation, which gives simple predictions for them. Studying large N-body simulations of such models with different force smoothing, we find that these two issues are in fact very closely related: our conclusion is that the accuracy of two point statistics in the non-linear regime starts to degrade strongly around the scale at which their behaviour deviates from that predicted by the stable clustering hypothesis. Physically the association of the two scales is in fact simple to understand: stable clustering fails to be a good approximation when there are strong interactions of structures (in particular merging) and it is precisely such non-linear processes which are sensitive to fluctuations at the smaller scales affected by discretisation. Resolution may be further degraded if the short distance gravitational smoothing scale is larger than the scale to which stable clustering can propagate. We examine in detail the very different conclusions of studies by Smith et al. (2003) and Widrow et al. (2009} and find that the strong deviations from stable clustering reported by these works are the results of over-optimistic assumptions about scales resolved accurately by the measured power spectra, and the reliance on Fourier space analysis. We emphasise the much poorer resolution obtained with the power spectrum compared to the two point correlation function..

Boundary terms and three-point functions: an AdS/CFT puzzle resolved

mathcal{N}=8 superconformal field theories, such as the ABJM theory at Chern-Simons level k = 1 or 2, contain 35 scalar operators {mathcal{O}}_{IJ} with Δ = 1 in the 35v representation of SO(8). The 3-point correlation function of these operators is non-vanishing, and indeed can be calculated non-perturbatively in the field theory. But its AdS4 gravity dual, obtained from gauged mathcal{N}=8 supergravity, has no cubic A3 couplings in its Lagrangian, where AIJ is the bulk dual of {mathcal{O}}_{IJ} . So conventional Witten diagrams cannot furnish the field theory result. We show that the extension of bulk supersymmetry to the AdS4 boundary requires the introduction of a finite A3 counterterm that does provide a perfect match to the 3-point correlator. Boundary supersymmetry also requires infinite counterterms which agree with the method of holographic renormalization. The generating functional of correlation functions of the Δ = 1 operators is the Legendre transform of the on-shell action, and the supersymmetry properties of this functional play a significant role in our treatment.

NIFTy cosmology: the clustering consistency of galaxy formation models

We present a clustering comparison of 12 galaxy formation models (including Semi-Analytic Models (SAMs) and Halo Occupation Distribution (HOD) models) all run on halo catalogues and merger trees extracted from a single {\Lambda}CDM N-body simulation. We compare the results of the measurements of the mean halo occupation numbers, the radial distribution of galaxies in haloes and the 2-Point Correlation Functions (2PCF). We also study the implications of the different treatments of orphan (galaxies not assigned to any dark matter subhalo) and non-orphan galaxies in these measurements. Our main result is that the galaxy formation models generally agree in their clustering predictions but they disagree significantly between HOD and SAMs for the orphan satellites. Although there is a very good agreement between the models on the 2PCF of central galaxies, the scatter between the models when orphan satellites are included can be larger than a factor of 2 for scales smaller than 1 Mpc/h. We also show that galaxy formation models that do not include orphan satellite galaxies have a significantly lower 2PCF on small scales, consistent with previous studies. Finally, we show that the 2PCF of orphan satellites is remarkably different between SAMs and HOD models. Orphan satellites in SAMs present a higher clustering than in HOD models because they tend to occupy more massive haloes. We conclude that orphan satellites have an important role on galaxy clustering and they are the main cause of the differences in the clustering between HOD models and SAMs.

Approximate Bayesian computation in large-scale structure: constraining the galaxy–halo connection

Standard approaches to Bayesian parameter inference in large scale structure assume a Gaussian functional form (chi-squared form) for the likelihood. This assumption, in detail, cannot be correct. Likelihood free inferences such as Approximate Bayesian Computation (ABC) relax these restrictions and make inference possible without making any assumptions on the likelihood. Instead ABC relies on a forward generative model of the data and a metric for measuring the distance between the model and data. In this work, we demonstrate that ABC is feasible for LSS parameter inference by using it to constrain parameters of the halo occupation distribution (HOD) model for populating dark matter halos with galaxies. Using specific implementation of ABC supplemented with Population Monte Carlo importance sampling, a generative forward model using HOD, and a distance metric based on galaxy number density, two-point correlation function, and galaxy group multiplicity function, we constrain the HOD parameters of mock observation generated from selected "true" HOD parameters. The parameter constraints we obtain from ABC are consistent with the "true" HOD parameters, demonstrating that ABC can be reliably used for parameter inference in LSS. Furthermore, we compare our ABC constraints to constraints we obtain using a pseudo-likelihood function of Gaussian form with MCMC and find consistent HOD parameter constraints. Ultimately our results suggest that ABC can and should be applied in parameter inference for LSS analyses.

A Gaussian theory for fluctuations in simple liquids.

Assuming an effective quadratic Hamiltonian, we derive an approximate, linear stochastic equation of motion for the density-fluctuations in liquids, composed of overdamped Brownian particles. From this approach, time dependent two point correlation functions (such as the intermediate scattering function) are derived. We show that this correlation function is exact at short times, for any interaction and, in particular, for arbitrary external potentials so that it applies to confined systems. Furthermore, we discuss the relation of this approach to previous ones, such as dynamical density functional theory as well as the formally exact treatment. This approach, inspired by the well known Landau-Ginzburg Hamiltonians, and the corresponding "Model B" equation of motion, may be seen as its microscopic version, containing information about the details on the particle level.

Towards 4-point correlation functions of any frac{1}{2} -BPS operators from supergravity

The quartic effective action for Kaluza-Klein modes that arises upon compactification of type IIB supergravity on the five-sphere S5 is a starting point for computing the four-point correlation functions of arbitrary weight frac{1}{2} -BPS operators in mathcal{N} = 4 super Yang-Mills theory in the supergravity approximation. The apparent structure of this action is rather involved, in particular it contains quartic terms with four derivatives which cannot be removed by field redefinitions. By exhibiting intricate identities between certain integrals involving spherical harmonics of S5 we show that the net contribution of these four-derivative terms to the effective action vanishes. Our result is in agreement with and provides further support to the recent conjecture on the Mellin space representation of the four-point correlation function of any frac{1}{2} -BPS operators in the supergravity approximation.

Detection of baryon acoustic oscillation features in the large-scale three-point correlation function of SDSS BOSS DR12 CMASS galaxies

We present the large-scale 3-point correlation function (3PCF) of the SDSS DR12 CMASS sample of $777,202$ Luminous Red Galaxies, the largest-ever sample used for a 3PCF or bispectrum measurement. We make the first high-significance ($4.5\sigma$) detection of Baryon Acoustic Oscillations (BAO) in the 3PCF. Using these acoustic features in the 3PCF as a standard ruler, we measure the distance to $z=0.57$ to $1.7\%$ precision (statistical plus systematic). We find $D_{\rm V}= 2024\pm29\;{\rm Mpc\;(stat)}\pm20\;{\rm Mpc\;(sys)}$ for our fiducial cosmology (consistent with Planck 2015) and bias model. This measurement extends the use of the BAO technique from the 2-point correlation function (2PCF) and power spectrum to the 3PCF and opens an avenue for deriving additional cosmological distance information from future large-scale structure redshift surveys such as DESI. Our measured distance scale from the 3PCF is fairly independent from that derived from the pre-reconstruction 2PCF and is equivalent to increasing the length of BOSS by roughly 10\%; reconstruction appears to lower the independence of the distance measurements. Fitting a model including tidal tensor bias yields a moderate significance ($2.6\sigma)$ detection of this bias with a value in agreement with the prediction from local Lagrangian biasing.

Mitigating the impact of the DESI fiber assignment on galaxy clustering

We present a simple strategy to mitigate the impact of an incomplete spectroscopic redshift galaxy sample as a result of fiber assignment and survey tiling. The method has been designed for the Dark Energy Spectroscopic Instrument (DESI) galaxy survey but may have applications beyond this. We propose a modification to the usual correlation function that nulls the almost purely angular modes affected by survey incompleteness due to fiber assignment. Predictions of this modified statistic can be calculated given a model of the two point correlation function. The new statistic can be computed with a slight modification to the data catalogues input to the standard correlation function code and does not incur any additional computational time. Finally we show that the spherically averaged baryon acoustic oscillation signal is not biased by the new statistic.

Are we living near the center of a local void?

The properties of the cosmic microwave background (CMB) temperature and polarisation anisotropies measured by a static, off-centered observer located in a local spherically symmetric void, are described. In particular in this paper we compute, together with the standard 2-point angular correlation functions, the off-diagonal correlators, which are no more vanishing by symmetry. While the energy shift induced by the off-centered position of the observer can be suppressed by a proper choice of the observer velocity, a lensing-like effect on the CMB emission point remains. This latter effect is genuinely geometrical (e.g. non-degenerate with a boost) and reflects in the structure of the off-diagonal correlators. At lowest order in this effect, the temperature and polarisation correlation matrices have non-vanishing diagonal elements, as usual, and all the off-diagonal terms are excited. This particular signature of a local void model allows one, in principle, to disentangle geometrical effects from local kinematical ones in CMB observations.

Modelling the large-scale redshift-space 3-point correlation function of galaxies

We present a configuration-space model of the large-scale galaxy 3-point correlation function (3PCF) based on leading-order perturbation theory and including redshift space distortions (RSD). This model should be useful in extracting distance-scale information from the 3PCF via the Baryon Acoustic Oscillation (BAO) method. We include the first redshift-space treatment of biasing by the baryon-dark matter relative velocity. Overall, on large scales the effect of RSD is primarily a renormalization of the 3PCF that is roughly independent of both physical scale and triangle opening angle; for our adopted $\Omega_{\rm m}$ and bias values, the rescaling is a factor of $\sim 1.8$. We also present an efficient scheme for computing 3PCF predictions from our model, important for allowing fast exploration of the space of cosmological parameters in future analyses.

Revisiting van der Waals like behavior of f(R) AdS black holes via the two point correlation function

Van der Waals like behavior of f(R) AdS black holes is revisited via two point correlation function, which is dual to the geodesic length in the bulk. The equation of motion constrained by the boundary condition is solved numerically and both the effect of boundary region size and f(R) gravity are probed. Moreover, an analogous specific heat related to δL is introduced. It is shown that the T−δL graphs of f(R) AdS black holes exhibit reverse van der Waals like behavior just as the T−S graphs do. Free energy analysis is carried out to determine the first order phase transition temperature T⁎ and the unstable branch in T−δL curve is removed by a bar T=T⁎. It is shown that the first order phase transition temperature is the same at least to the order of 10−10 for different choices of the parameter b although the values of free energy vary with b. Our result further supports the former finding that charged f(R) AdS black holes behave much like RN-AdS black holes. We also check the analogous equal area law numerically and find that the relative errors for both the cases θ0=0.1 and θ0=0.2 are small enough. The fitting functions between log⁡|T−Tc| and log⁡|δL−δLc| for both cases are also obtained. It is shown that the slope is around 3, implying that the critical exponent is about 2/3. This result is in accordance with those in former literatures of specific heat related to the thermal entropy or entanglement entropy.

Nucleon-pion-state contribution in lattice calculations of moments of parton distribution functions

We employ chiral perturbation theory to calculate the nucleon-pion-state contribution to the 3-point correlation functions measured in lattice QCD to compute various moments of parton distribution functions (quark momentum fraction, helicity and transversity moment). We estimate the impact of the nucleon-pion-state contribution on the plateau method for lattice simulations with a physical pion mass. The nucleon-pion-state contribution results in an overestimation of all three moments. The overestimation is at the 5--20% level for source-sink separations of about 1.5 fm.

The large-scale three-point correlation function of the SDSS BOSS DR12 CMASS galaxies

We report a measurement of the large-scale 3-point correlation function of galaxies using the largest dataset for this purpose to date, 777, 202 Luminous Red Galaxies in the Sloan Digital Sky Survey Baryon Acoustic Oscillation Spectroscopic Survey (SDSS BOSS) DR12 CMASS sample. This work exploits the novel algorithm of Slepian & Eisenstein (2015b) to compute the multipole moments of the 3PCF in $\mathcal{O}(N^2)$ time, with $N$ the number of galaxies. Leading-order perturbation theory models the data well in a compressed basis where one triangle side is integrated out. We also present an accurate and computationally efficient means of estimating the covariance matrix. With these techniques the redshift-space linear and non-linear bias are measured, with 2.6% precision on the former if $\sigma_8$ is fixed. The data also indicates a $2.8\sigma$ preference for the BAO, confirming the presence of BAO in the 3-point function.

On the impact of large angle CMB polarization data on cosmological parameters

We study the impact of the large-angle CMB polarization datasets publicly released by the WMAP and Planck satellites on the estimation of cosmological parameters of the ΛCDM model. To complement large-angle polarization, we consider the high resolution (or "high-ℓ") CMB datasets from either WMAP or Planck as well as CMB lensing as traced by Planck's measured four point correlation function. In the case of WMAP, we compute the large-angle polarization likelihood starting over from low resolution frequency maps and their covariance matrices, and perform our own foreground mitigation technique, which includes as a possible alternative Planck 353 GHz data to trace polarized dust. We find that the latter choice induces a downward shift in the optical depth τ, roughly of order 2σ, robust to the choice of the complementary high resolution dataset. When the Planck 353 GHz is consistently used to minimize polarized dust emission, WMAP and Planck 70 GHz large-angle polarization data are in remarkable agreement: by combining them we find τ = 0.066 +0.012−0.013, again very stable against the particular choice for high-ℓ data. We find that the amplitude of primordial fluctuations As, notoriously degenerate with τ, is the parameter second most affected by the assumptions on polarized dust removal, but the other parameters are also affected, typically between 0.5 and 1σ. In particular, cleaning dust with Planck's 353 GHz data imposes a 1σ downward shift in the value of the Hubble constant H0, significantly contributing to the tension reported between CMB based and direct measurements of the present expansion rate. On the other hand, we find that the appearance of the so-called low ℓ anomaly, a well-known tension between the high- and low-resolution CMB anisotropy amplitude, is not significantly affected by the details of large-angle polarization, or by the particular high-ℓ dataset employed.

Bell violation in the sky

In this work, we have studied the possibility of setting up Bell’s inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in the presence of additional time-dependent mass contribution in the cosmological perturbation theory. Here for completeness we compute the total number density and the energy density of the newly created particles in terms of the Bogoliubov coefficients using the WKB approximation method. Next using the background scalar fluctuation in the presence of a new time-dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for a one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model-independent way without any prior knowledge of primordial gravitational waves. Also using the input from a newly introduced cosmological parameter, we finally give a theoretical estimate for the tensor-to-scalar ratio in a model-independent way. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in a cosmological Bell violating test experiment. Further, we cite a precise example of this setup applicable in the context of string theory motivated axion monodromy model. Then we comment on the explicit role of the decoherence effect and high spin on cosmological Bell violating test experiment. Finally, we provide a theoretical bound on the heavy particle mass parameter for scalar fields, gravitons and other high spin fields from our proposed setup.

An induced real quaternion spherical ensemble of random matrices

We study the induced spherical ensemble of non-Hermitian matrices with real quaternion entries (considering each quaternion as a [Formula: see text] complex matrix). We define the ensemble by the matrix probability distribution function that is proportional to [Formula: see text] These matrices can also be constructed via a procedure called ‘inducing’, using a product of a Wishart matrix (with parameters [Formula: see text]) and a rectangular Ginibre matrix of size [Formula: see text]. The inducing procedure imposes a repulsion of eigenvalues from [Formula: see text] and [Formula: see text] in the complex plane with the effect that in the limit of large matrix dimension, they lie in an annulus whose inner and outer radii depend on the relative size of [Formula: see text], [Formula: see text] and [Formula: see text]. By using functional differentiation of a generalized partition function, we make use of skew-orthogonal polynomials to find expressions for the eigenvalue [Formula: see text]-point correlation functions, and in particular the eigenvalue density (given by [Formula: see text]). We find the scaled limits of the density in the bulk (away from the real line) as well as near the inner and outer annular radii, in the four regimes corresponding to large or small values of [Formula: see text] and [Formula: see text]. After a stereographic projection, the density is uniform on a spherical annulus, except for a depletion of eigenvalues on a great circle corresponding to the real axis (as expected for a real quaternion ensemble). We also form a conjecture for the behavior of the density near the real line based on analogous results in the [Formula: see text] and [Formula: see text] ensembles; we support our conjecture with data from Monte Carlo simulations of a large number of matrices drawn from the [Formula: see text] induced spherical ensemble. This ensemble is a quaternionic analog of a model of a one-component charged plasma on a sphere, with soft wall boundary conditions.

Noninteracting fermions at finite temperature in ad-dimensional trap: Universal correlations

We study a system of $N$ non-interacting spin-less fermions trapped in a confining potential, in arbitrary dimensions $d$ and arbitrary temperature $T$. The presence of the trap introduces an edge where the average density of fermions vanishes. Far from the edge, near the center of the trap (the so called "bulk regime"), physical properties of the fermions have traditionally been understood using the Local Density Approximation. However, this approximation drastically fails near the edge where the density vanishes. In this paper we show that, even near the edge, novel universal properties emerge, independently of the details of the confining potential. We show that for large $N$, these fermions in a confining trap, in arbitrary dimensions and at finite temperature, form a determinantal point process. As a result, any $n$-point correlation function can be expressed as an $n \times n$ determinant whose entry is called the kernel. Near the edge, we derive the large $N$ scaling form of the kernels. In $d=1$ and $T=0$, this reduces to the so called Airy kernel, that appears in the Gaussian Unitary Ensemble (GUE) of random matrix theory. In $d=1$ and $T>0$ we show a remarkable connection between our kernel and the one appearing in the $1+1$-dimensional Kardar-Parisi-Zhang equation at finite time. Consequently our result provides a finite $T$ generalization of the Tracy-Widom distribution, that describes the fluctuations of the rightmost fermion at $T=0$. In $d>1$ and $T \geq 0$, while the connection to GUE no longer holds, the process is still determinantal whose analysis provides a new class of kernels, generalizing the $1d$ Airy kernel at $T=0$ obtained in random matrix theory. Some of our finite temperature results should be testable in present-day cold atom experiments, most notably our detailed predictions for the temperature dependence of the fluctuations near the edge.

Probing cosmological isotropy with Planck Sunyaev–Zeldovich galaxy clusters

We probe the statistical isotropy hypothesis of the large-scale structure with the second Planck Sunyaev-Zeldovich (PSZ2) galaxy clusters data set. Our analysis adopts a statistical-geometrical method which compares the 2-point angular correlation function of objects in antipodal patches of the sky. Given possible observational biases, such as the presence of anisotropic sky cuts and the non-uniform exposure of Planck's instrumentation, ensembles of Monte Carlo realisations are produced in order to assess the significance of our results. When these observational effects are properly taken into account, we find neither evidence for preferred directions in the sky nor signs of large-angle features in the galaxy clusters celestial distribution. The PSZ2 data set is, therefore, in good concordance with the fundamental hypothesis of large-angle isotropy of cosmic objects.