Correlation function

A function that quantifies statistical or quantum relationships between values of a field at different points, often depending on their separation.

Random variable: A quantity whose value is determined by the outcome of a random process. Field values are treated as random variables when their statistical dependence is measured.
Two-point correlation function: A function giving the correlation between field values at two specified points. It is the simplest nontrivial member of the correlation-function hierarchy.
Dynamic structure factor: A frequency- and wave-vector-resolved measure of density fluctuations in a material. It is the Fourier-space density correlation measured in scattering experiments.
Autocorrelation: A measure of how a signal relates to a shifted or delayed version of itself. It is a same-field special case, while general correlations can compare different fields.
Expectation value: The probability-weighted average of a quantity over possible outcomes. Correlation functions are built from averages of products of field values.
Connected correlation function: A correlation function with contributions from independent subsets removed. It isolates correlations that cannot be factored into lower-order pieces.
Structure factor: A wave-vector-dependent measure of spatial correlations among particles or density fluctuations. It summarizes the spatial correlation function in reciprocal space.
Cross-correlation: A measure of statistical dependence between two distinct signals or fields. It compares different quantities rather than correlating one field with itself.
Covariance: A measure of how two random variables vary together, subtracting the product of their means. Unlike an unconnected correlation, covariance removes contributions from nonzero means.
Wick's theorem: A rule expressing Gaussian-field correlation functions as sums of products of two-point functions. It reduces higher-order correlations to pairings when the field is Gaussian.

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