Two-point Correlation Function and Power Spectrum at Very Large Scales

2005 ◽  
Vol 201 ◽  
pp. 449-450
Author(s):  
Z.-G. Deng ◽  
X.-Y. Xia
Keyword(s):  
Correlation Function ◽  
Power Spectrum ◽  
Correlation Functions ◽  
Large Scale ◽  
Wave Number ◽  
Scale Fluctuation ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Large Scale Fluctuation

Subsamples of galaxies with different morphological types have been sorted out from Stromlo-APM redshift survey. Two-point correlation function for each subsample has been calculated. The two-point correlation functions for all subsamples show very large scale fluctuation. We show that the two-point correlation function with fluctuation could be fitted by a modified power spectrum with power excess at wave number comparable to the scale of the fluctuation.

scholarly journals The Anglo-Australian Redshift Survey

1983 ◽  
Vol 104 ◽  
pp. 175-175
Author(s):  
J. Bean ◽  
G. Efstathiou ◽  
R. S. Ellis ◽  
B. A. Peterson ◽  
T. Shanks ◽  
...  
Keyword(s):  
Correlation Function ◽  
Luminosity Function ◽  
Large Scale ◽  
Peculiar Velocities ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Density Inhomogeneities ◽  
The Universe

The aim of the survey is to sample a relatively large, randomly chosen volume of the Universe in order to study the large-scale distribution of galaxies using the two-point correlation function, the peculiar velocities between galaxy pairs and to provide an estimate of the galaxian luminosity function that is unaffected by density inhomogeneities and Virgo infall.

scholarly journals Large-Scale Structure in the Durham/Ukst Galaxy Redshift Survey

1994 ◽  
Vol 161 ◽  
pp. 693-697
Author(s):  
A. Broadbent ◽  
T. Shanks ◽  
F.G. Watson ◽  
Q.A. Parker ◽  
R. Fong ◽  
...  
Keyword(s):  
Correlation Function ◽  
Statistical Analysis ◽  
Large Scale ◽  
Large Scale Structure ◽  
Scale Structure ◽  
Point Correlation ◽  
Point Correlation Function ◽  
Redshift Survey ◽  
Galaxy Redshift ◽  
The Universe

We report on the progress of the compilation and analysis of the Durham/UKST galaxy redshift survey. This survey will probe a large contiguous volume of space within a 1500 sq. deg. area of sky around the SGP. It will contain redshifts of ∼ 4000 galaxies of bJ < 17m providing detailed information about the structure of the Universe on large scales. Large features on scales of ∼ 100h−1 Mpc are clearly visible on examination of the completed section of the survey, although a statistical analysis of the survey by means of the two-point correlation function is close to zero on scales of r > 10h−1 Mpc.

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 Cosmological Spectrum of Two-Point Correlation Function from Vacuum Fluctuation of Stringy Axion Field in De Sitter Space: A Study of the Role of Quantum Entanglement

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 79
Author(s):  
Sayantan Choudhury ◽  
Sudhakar Panda
Keyword(s):  
Correlation Function ◽  
Power Spectrum ◽  
Quantum Entanglement ◽  
De Sitter Space ◽  
Entangled State ◽  
De Sitter ◽  
Vacuum Fluctuation ◽  
Axion Field ◽  
Point Correlation ◽  
Point Correlation Function

In this work, we study the impact of quantum entanglement on the two-point correlation function and the associated primordial power spectrum of mean square vacuum fluctuation in a bipartite quantum field theoretic system. The field theory that we consider is the effective theory of axion field arising from Type IIB string theory compacted to four dimensions. We compute the expression for the power spectrum of vacuum fluctuation in three different approaches, namely (1) field operator expansion (FOE) technique with the quantum entangled state, (2) reduced density matrix (RDM) formalism with mixed quantum state and (3) the method of non-entangled state (NES). For a massless axion field, in all three formalisms, we reproduce, at the leading order, the exact scale invariant power spectrum which is well known in the literature. We observe that due to quantum entanglement, the sub-leading terms for these thee formalisms are different. Thus, such correction terms break the degeneracy among the analysis of the FOE, RDM and NES formalisms in the super-horizon limit. On the other hand, for massive axion field we get a slight deviation from scale invariance and exactly quantify the spectral tilt of the power spectrum in small scales. Apart from that, for massless and massive axion field, we find distinguishable features of the power spectrum for the FOE, RDM, and NES on the large scales, which is the result of quantum entanglement. We also find that such large-scale effects are comparable to or greater than the curvature radius of the de Sitter space. Most importantly, in near future if experiments probe for early universe phenomena, one can detect such small quantum effects. In such a scenario, it is possible to test the implications of quantum entanglement in primordial cosmology.

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 N-body Simulations to Test the Reliability of Two-point Correlation Functions of Galaxies

1992 ◽  
Vol 9 ◽  
pp. 703-704
Author(s):  
Yasushi Suto
Keyword(s):  
Correlation Functions ◽  
Large Scale ◽  
Sample Volume ◽  
Limited Data ◽  
Observable Universe ◽  
Large N ◽  
The Galaxy ◽  
Point Correlation ◽  
Systematic Biases ◽  
Redshift Survey

The shape and amplitude of the galaxy – galaxy correlation functions, ξgg(r), are among the most widely used measures of the large-scale structure in the universe (Totsuji & Kihara 1969). The estimates, however, might be seriously affected by the limited size of the sample volume, or equivalently, the limited number of available galaxies. In fact, while the observable universe extends c/H0 ~ 3000h-1Mpc, most observational works to map the distribution of galaxies so far have been mainly applied to samples within ~ 100h-1Mpc from us. Thus a CfA redshift survey slice, for example, of 8h < α < 17h, 26.5° < δ < 32.5°, and cz ≾ 15000km/sec (de Lapparent et al. 1986, 1988) represents merely ~ 2 x 10-5 of the total volume of the observable universe. This clearly illustrates the importance of examining possible systematic biases and variations in the estimates of two-point correlation functions from instrinsically limited data. We studied such sample-to-sample variations by analysing subsamples extracted from large N-body simulation data.

scholarly journals The 2dF QSO Redshift Survey - XIV. Structure and evolution from the two-point correlation function

2005 ◽  
Vol 356 (2) ◽  
pp. 415-438 ◽  
Author(s):  
Scott M. Croom ◽  
B. J. Boyle ◽  
T. Shanks ◽  
R. J. Smith ◽  
L. Miller ◽  
...  
Keyword(s):  
Correlation Function ◽  
Point Correlation ◽  
Point Correlation Function ◽  
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.

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