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Everything about Correlation function
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 those variables. If one considers the correlation function between random variables representing the same quantity measured at two different points, then this is often referred to as an autocorrelation function, which is made up of autocorrelations. Correlation functions of different random variables are sometimes called cross-correlation functions to emphasize that different variables are being considered and because they are made up of cross-correlations. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Correlation functionA 5-minute orientation
- Skim a recent paper: Single-cell atlas reveals correlates of high cognitive function, dementia, and resilience to Alzheimer’s disease pathologyInfluential work since 2022
- Pick up a classic book: Periodically correlated random sequencesThe most-reprinted book on the subject
- Read the landmark paper: Development of the Colle-Salvetti correlation-energy formula into a functional of the electron densityCited 97,734 times
- Go sideways: Partition function (mathematics)A closely related topic
- Go sideways: Cross-correlation matrixA closely related topic
đź“– Definitions
Noun function giving the statistical correlation between random variables at two different points in space or time
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
Density-functional approximation for the correlation energy of the inhomogeneous electron gas
A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)
Results obtained with the correlation energy density functionals of becke and Lee, Yang and Parr
🆕 Influential since 2022
Single-cell atlas reveals correlates of high cognitive function, dementia, and resilience to Alzheimer’s disease pathology
Femtoscopic correlation function for the Tcc(3875)+ state
Correlation function for the $$a_0(980)$$
A study of the Ď•N correlation function
Structure–Function Correlation in Cobalt-Induced Brain Toxicity
đź“š Books worth reading
Periodically correlated random sequencesHarry L. Hurd, Abolghassem Miamee · 2007
Multivariate characteristic and correlation functionsZoltán Sasvári · 2013- 📕Towards a rational model for the triple velocity correlations of turbulenceB. A. Younis · 1999
- 📕Alice and Bob Meet BanachGuillaume Aubrun, Stanislaw J. Szarek · 2017
- 📕Scientific papers from Department of Mathematics for the year 1928-[1932]Lehigh University. Department of Mathematics · 1929
- 📕The correlation functions in the theory of superconductivityBogoli͡ubov, N. N. · 1967
- 📕Performance enhancement of a joint transform correlator using the directionality of a spatial light modulatorNational Institute of Standards and Technology (U.S.) · 1998
- 📕Directionality of an electrically-addressable spatial light modulator and its application to a joint transform correlatorNational Institute of Standards and Technology (U.S.) · 1998
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Partition function (mathematics) The partition function or configuration integral, as used in probability theory, information theory and dynamical systems, is a generalization of the definition…
- Cross-correlation matrix The cross-correlation matrix of two random vectors is a matrix containing as elements the cross-correlations of all pairs of elements of the random vectors…
- Autocorrelation Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself. Essentiall…
- Covariance matrix In probability theory and statistics, a covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance…
- Multivariate random variable In probability and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown…
- Cross-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…
- White noise In signal processing, white noise is a random signal having equal intensity at different frequencies, giving it a constant power spectral density. The…
- Quantum state In quantum physics, a quantum state is a mathematical entity that represents a physical system. Quantum mechanics specifies the construction, evolution…