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Correlation as a function of distance
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between
Correlation_function
Covariance and correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This is
Cross-correlation
Function describing the distribution of galaxies in the universe
astronomy, a correlation function describes the distribution of objects (often stars or galaxies) in the universe. By default, "correlation function" refers
Correlation function (astronomy)
Correlation_function_(astronomy)
Measure of a system's order
the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Topics referred to by the same term
Correlation function may refer to: Correlation function, correlation between random variables at two different points in space or time Correlation function
Correlation function (disambiguation)
Correlation_function_(disambiguation)
Statistical relationship
correlation coefficient Cophenetic correlation Correlation disattenuation Correlation function Correlation gap Covariance Covariance and correlation Cross-correlation
Correlation
Measure of linear correlation
In statistics, the Pearson correlation coefficient (PCC), also known as Pearson's r, the Pearson product-moment correlation coefficient (PPMCC), or simply
Pearson correlation coefficient
Pearson_correlation_coefficient
Measure of the projected clustering of galaxies
The angular correlation function is a function which measures the projected clustering of galaxies, due to discrepancies between their actual and expected
Angular_correlation_function
Nonparametric measure of rank correlation
described using a monotonic function. The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Expectation value of time-ordered quantum operators
In quantum field theory, correlation functions, often referred to as correlators or Green's functions, are vacuum expectation values of time-ordered products
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Correlation of a signal with a time-shifted copy of itself, as a function of shift
complex random process is the Pearson correlation between values of the process at different times, as a function of the two times or of the time lag.
Autocorrelation
Theoretical framework in physics
propagator, two-point correlation function, two-point Green's function or two-point function for short. The free two-point function, also known as the Feynman
Quantum_field_theory
Impulse response associated with auditory processing
A reverse correlation function, also known as a revcor function, is an impulse response function associated with the processing of hearing in the peripheral
Reverse_correlation_function
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Equation in statistical mechanics
The OZ equation relates the pair correlation function to the direct correlation function. The direct correlation function is only used in connection with
Ornstein–Zernike_equation
Concept in quantum optics
In quantum optics, correlation functions are used to characterize the statistical and coherence properties – the ability of waves to interfere – of electromagnetic
Higher_order_coherence
Mathematical conjecture
correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the Riemann zeta function (normalized
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Computational quantum mechanical modelling method to investigate electronic structure
in the direct correlation function between two particles c 2 {\displaystyle c_{2}} . The direct correlation function is the correlation contribution to
Density_functional_theory
Method of solution to differential equations
the role of propagators, also referred to as two-point (correlation) functions. A Green's function, G(x,s), of a linear differential operator L = L(x) acting
Green's_function
Generating function for quantum correlation functions
In quantum field theory, partition functions are generating functionals for correlation functions, making them key objects of study in the path integral
Partition function (quantum field theory)
Partition_function_(quantum_field_theory)
Concept in digital signal processing
Correlation does not imply causation Covariance function Pearson product-moment correlation coefficient Correlation function (astronomy) Correlation function
Cross-correlation_matrix
Numerical measure of a statistical relationship between variables
A correlation coefficient is a numerical measure of some type of linear correlation, meaning a linear function between two variables. The variables may
Correlation_coefficient
Quantum version of the classical action
also acts as a generating functional for one-particle irreducible correlation functions. The potential component of the effective action is called the effective
Effective_action
Pulse-shaping filter in digital modulation
B=2BW=R_{S}(\beta +1),\quad (0<\beta <1)} The auto-correlation function of raised cosine function is as follows: R ( τ ) = T [ sinc ( τ T ) cos (
Raised-cosine_filter
Function in condensed matter physics
dynamical structure factor) is a mathematical function that contains information about inter-particle correlations and their time evolution. It is a generalization
Dynamic_structure_factor
Concepts in probability and statistics
linear function of the other with respectively a positive (or negative) slope. Although the values of the theoretical covariances and correlations are linked
Covariance_and_correlation
Pictorial representation of the behavior of subatomic particles
representation of a perturbative contribution to the transition amplitude or correlation function of a quantum mechanical or statistical field theory. Within the canonical
Feynman_diagram
Generalization of the concept from statistical mechanics
This allows, for example, the partition function to be used as a generating function for correlation functions. This is discussed in greater detail below
Partition function (mathematics)
Partition_function_(mathematics)
space (i.e., as a function of spatial frequency). The FSC is the three-dimensional extension of the two-dimensional Fourier ring correlation (FRC); also known
Fourier_shell_correlation
Quantum field theory enjoying conformal symmetry
context of correlation functions, and may be viewed as efficient notations for writing axioms for correlation functions. Correlation functions depend linearly
Conformal_field_theory
Two-dimensional state of matter
determined with the translational correlation function G G → ( R → ) {\displaystyle G_{\vec {G}}({\vec {R}})} as function of the distance between lattice
Hexatic_phase
Correlators of field operators
many-body theory, the term Green's function (or Green function) is sometimes used interchangeably with correlation function, but refers specifically to correlators
Green's function (many-body theory)
Green's_function_(many-body_theory)
Conjecture on zeros of the zeta function
pair correlation conjecture that the correlation functions of the (suitably normalized) zeros of the zeta function should be the same as those of the eigenvalues
Riemann_hypothesis
Topics referred to by the same term
to: Correlation function (quantum field theory) An optical correlator A radio correlator An apparatus for measuring second-order correlation function of
Correlator
Equation relating transport coefficients to correlation functions
{\displaystyle \gamma } in terms of the integral of the equilibrium time correlation function of the time derivative of a corresponding microscopic variable A
Green–Kubo_relations
Conformal field theory on a 2D spacetime
commute, but also their correlation functions are multivalued. The torus partition function is a particular correlation function that depends solely on
Two-dimensional conformal field theory
Two-dimensional_conformal_field_theory
Concept in probability theory and statistics
In probability theory and statistics, partial correlation measures the degree of association between two random variables, with the effect of a set of
Partial_correlation
Topological quantum field theory
normalized correlation function by dividing this observable by the partition function Z(M), which is just the 0-point correlation function. In the special
Chern–Simons_theory
Fluctuations in the density of the normal matter of the universe
galaxies by calculating a two-point correlation function on the data. The correlation function (ξ) is a function of comoving galaxy separation distance
Baryon_acoustic_oscillations
Signal with properties that vary cyclically with time
exhibit periodic statistical properties. The Spectral Correlation Function highlights correlations between frequencies separated by a cyclic frequency α
Cyclostationary_process
Resistance of a fluid to shear deformation
Green–Kubo relations for the linear shear viscosity or the transient time correlation function expressions derived by Evans and Morriss in 1988. Although these
Viscosity
Techniques to study geometric data
the recent methods is presented by Tahmasebi et al. uses a cross-correlation function to improve the spatial pattern reproduction. They call their MPS
Spatial_analysis
In statistical mechanics, an Ursell function or connected correlation function, is a cumulant of a random variable. It can often be obtained by summing
Ursell_function
Two-dimensional conformal field theory
duality b → 1 b , {\displaystyle b\to {\frac {1}{b}}\ ,} The correlation functions of Liouville theory are covariant under this duality, and under
Liouville_field_theory
Potential for two waves to interfere
mathematical definition of the degree of coherence is given by means of correlation functions. More broadly, coherence describes the statistical similarity of
Coherence_(physics)
The spectral correlation density (SCD), sometimes also called the cyclic spectral density or spectral correlation function, is a function that describes
Spectral_correlation_density
Quantum electromechanical process
solution must take the form of a two-time correlation function as opposed to the above one-time correlation function. This solution appears as ⟨ σ + ( 0 )
Resonance_fluorescence
Stochastic differential equation
{\boldsymbol {\eta }}(t)} has a Gaussian probability distribution with correlation function ⟨ η i ( t ) η j ( t ′ ) ⟩ = 2 λ k B T δ i , j δ ( t − t ′ ) , {\displaystyle
Langevin_equation
Gravitational deflection of light
component at 45°. These correlation functions are typically computed by averaging over many pairs of galaxies. The last correlation function, ξ × + {\displaystyle
Weak_gravitational_lensing
Method of statistical physics
A correlation function is used as a scalar product, which is why the formalism can also be used for analyzing the dynamics of correlation functions. A
Mori–Zwanzig_formalism
Statistical physics theorem
{\displaystyle \langle x(t)\rangle } yields where A(t) is the auto-correlation function of x in the absence of a field: A ( t ) = ⟨ [ x ( t ) − ⟨ x ⟩ 0 ]
Fluctuation–dissipation theorem
Fluctuation–dissipation_theorem
Function that preserves distinctness
In mathematics, an injective function (also known as injection, or one-to-one function) is a function f that maps distinct elements of its domain to distinct
Injective_function
Presence/absence of symmetry or correlation in a many-particle system
correlated behavior. This can be expressed as a correlation function, namely the spin-spin correlation function: G ( x , x ′ ) = ⟨ s ( x ) , s ( x ′ ) ⟩ .
Order_and_disorder
as the memory function. The value of X ¯ {\displaystyle {\bar {X}}} and the function F(r) contain all the information about correlation properties of
Additive_Markov_chain
Function in probability theory
exponential and squared exponential covariance functions as special cases. Autocorrelation function Correlation function Covariance matrix Covariance operator –
Covariance_function
Mathematical conjecture
forces interact, a three-point function called the Yukawa coupling is introduced which acts as the correlation function for states in H 1 ( X , Ω X 1 )
Mirror_symmetry_conjecture
Type of operator expectation value
the Casimir effect. This concept is important for working with correlation functions in quantum field theory. In the context of spontaneous symmetry
Vacuum_expectation_value
Matrix-valued random variable
x_{n}),} which are skew symmetric functions of their variables. In particular, the one-point correlation function, or density of states, is R n , V (
Random_matrix
Technique to find image offset
Phase correlation is an approach to estimate the relative translative offset between two similar images (digital image correlation) or other data sets
Phase_correlation
Medical imaging technique of the heart
cross correlation function crosses zero. As shown in the right figure, parabolic fit can help find the real peak of the cross correlation function. The
Doppler_echocardiography
Way of inferring information from cross-covariance matrices
are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y that have a maximum correlation with
Canonical_correlation
Analytical technique
coherent speckle pattern fluctuates in time, one can measure a time correlation function, and thus measure the timescale processes of interest (diffusion
X-ray photon correlation spectroscopy
X-ray_photon_correlation_spectroscopy
wave functions or more complicated objects, and therefore it is interpreted as a correlation function. For instance, if the curvature function is the
Curvature renormalization group method
Curvature_renormalization_group_method
Evolutionary equation under renormalization group flow
of the n-point correlation functions under variation of the energy scale at which the theory is defined and involves the beta function of the theory and
Callan–Symanzik_equation
Partial differential equations of correlation functions
KZ equations, are linear differential equations satisfied by the correlation functions (on the Riemann sphere) of two-dimensional conformal field theories
Knizhnik–Zamolodchikov equations
Knizhnik–Zamolodchikov_equations
Statistical measure
In statistics and in probability theory, distance correlation is a measure of dependence between two paired random vectors of arbitrary, not necessarily
Distance_correlation
Effective particle coupling beyond tree level
perturbation theory. In particular, it is the one particle irreducible correlation function involving the fermion ψ {\displaystyle \psi } , the antifermion ψ
Vertex_function
Cryptographic attack
(LFSRs) using a Boolean function. Correlation attacks exploit a statistical weakness that arises from the specific Boolean function chosen for the keystream
Correlation_attack
Phenomenon in quantum optics
-\langle a^{\dagger }a\rangle ^{2}.} The second-order intensity correlation function (for zero delay time) is defined as g ( 2 ) ( 0 ) = ⟨ ( a † ) 2 a
Photon_antibunching
Associative algebra generalizing the Virasoro algebra
algebras. In this article, the sections on representation theory and correlation functions apply to freely generated W-algebras. While it is possible to construct
W-algebra
Equation describing the universe's density contrast
density and the mean density) as a function of scale. It is the Fourier transform of the matter correlation function. On large scales, gravity competes
Matter_power_spectrum
No spontaneous symmetry breaking in two-dimensional systems at finite temperature
Goldstone bosons, being massless, would have an infrared divergent correlation function. The absence of spontaneous symmetry breaking in d ≤ 2 dimensional
Mermin–Wagner_theorem
Gravitational wave detection tool
angular separation on the sky as seen from Earth. This theoretical correlation function assumes Einstein's general relativity and a gravitational wave background
Hellings–Downs_curve
Topics referred to by the same term
Correlations (album), a 1979 album by Ashra Correlation function (disambiguation) All pages with titles containing correlation This disambiguation page lists articles
Correlation_(disambiguation)
signal-to-noise ratio, and at a microsecond time scale. The normalized cross-correlation function is defined for two fluorescent species, G and R, which are independent
Fluorescence cross-correlation spectroscopy
Fluorescence_cross-correlation_spectroscopy
Concept in probability and statistics
series analysis) to normalize the autocovariance function to get a time-dependent Pearson correlation coefficient. However in other disciplines (e.g. engineering)
Autocovariance
Sequence of data points over time
function and the spectral density function (also cross-correlation functions and cross-spectral density functions) Scaled cross- and auto-correlation
Time_series
The triple correlation of an ordinary function on the real line is the integral of the product of that function with two independently shifted copies of
Triple_correlation
constant kAB for the transition from A to B is derived from the correlation function C ( t ) = ⟨ h A ( 0 ) h B ( t ) ⟩ ⟨ h A ⟩ {\displaystyle C(t)={\frac
Transition_path_sampling
When a radio signal reaches a remote receiver
(third plot) is the cross-correlation function ( P 1 ⋆ P 0 ) {\displaystyle (P_{1}\star P_{0})} . The cross-correlation function slides one curve in time
Time_of_arrival
autocorrelation function or cross-correlation function, depends on the lag-time between the times being considered. Typically such functions, ρ(t), decay
Life-time_of_correlation
Special class of quantum states
covariance, which are equivalent to its one-point and two-point correlation functions. The Wigner quasiprobability distribution of a bosonic Gaussian
Gaussian_state
Conformal field theory of the 2D Ising model critical point
the central charge c = 1 2 {\displaystyle c={\tfrac {1}{2}}} . Correlation functions of the spin and energy operators are described by the ( 4 , 3 )
Two-dimensional critical Ising model
Two-dimensional_critical_Ising_model
Quantum chromodynamics on a lattice
region non-perturbative methods, such as Monte-Carlo sampling of the correlation function, are necessary. Lattice perturbation theory can also provide results
Lattice_QCD
Solution theory
mechanics, the KB theory derives thermodynamic quantities from pair correlation functions between all molecules in a multi-component solution. The KB theory
Kirkwood–Buff_solution_theory
Statistical estimator
parameter requires the knowledge of parameter correlation function. If the knowledge of this correlation function is not perfectly available, a popular minimax
Minimax_estimator
Function in quantum field theory showing probability amplitudes of moving particles
nonlocal correlation in these vacuum fluctuations, analogous to an EPR correlation. Indeed, the propagator is often called a two-point correlation function for
Propagator
definition of the pair correlation function, which gives a way to statistically quantify the strength of interaction or correlation between points of a point
Factorial_moment_measure
Method in computational chemistry
correlation function, accounts for the effects of a third particle in a system. The indirect correlation function is given as the direct correlation function
Solvent_model
Special functions used to build correlation functions in 2D CFTs
(named after Miguel Ángel Virasoro) are special functions that serve as building blocks of correlation functions. On a given punctured Riemann surface, Virasoro
Virasoro_conformal_block
Inequalities satisfied by the correlation functions
A correlation inequality is any of a number of inequalities satisfied by the correlation functions of a model. Such inequalities are of particular use
Correlation_inequality
Theorem for reducing high-order derivatives
theorem applied to fields is proved in essentially the same way. The correlation function that appears in quantum field theory can be expressed by a contraction
Wick's_theorem
Equations for correlation functions in QFT
Julian Schwinger and Freeman Dyson, are general relations between correlation functions in quantum field theories (QFTs). They are also referred to as the
Schwinger–Dyson_equation
Quantum correlations related to wave-particle duality
Hanbury Brown and Twiss (HBT) effect is any of a variety of correlation and anti-correlation effects in the intensities received by two detectors from a
Hanbury Brown and Twiss effect
Hanbury_Brown_and_Twiss_effect
Integral expressing the amount of overlap of one function as it is shifted over another
'shape' of one function is modified by the other. Some features of convolution are similar to cross-correlation: for real-valued functions, of a continuous
Convolution
Collection of models with the same renormalization group flow limit
{\displaystyle \eta } measures the size of correlations at the critical temperature. It is defined so that the correlation function of the order parameter scales as
Universality_class
Euclidean Wightman distributions
Schrader). Schwinger functions are also referred to as Euclidean correlation functions. Here we describe Osterwalder–Schrader (OS) axioms for a Euclidean
Schwinger_function
Measure of covariance of components of a random vector
related to the covariance matrix is the matrix of Pearson product-moment correlation coefficients between each of the random variables in the random vector
Covariance_matrix
Relative importance of certain frequencies in a composite signal
{\displaystyle T\to \infty } becomes the Fourier transform of a cross-correlation function. S x y ( f ) = ∫ − ∞ ∞ [ lim T → ∞ 1 T ∫ − ∞ ∞ x T ∗ ( t − τ ) y
Spectral_density
American astronomer (born 1965)
completed his senior thesis, titled "Simulating the measurement of the correlation function of the Shane–Wirtanen galaxy counts", under the supervision of Edward
Michael_E._Brown
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