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Correlation functions contain information about the distribution of points or events, or things across some space/time.
A very simple example of a correlation function is the following. Given the existence of a point at a position X in some space, what is the probability of there being another point at a second position Y.
For [[stochastic process]]es, including those that arise in [[statistical mechanics]] and Euclidean [[quantum field theory]], a '''correlation function''' is the [[correlation]] between [[random variable]]s at two different points in space or time. If one considers the correlation function between random variables at the same point but at two different times then one refers to this as the '''autocorrelation function'''. If there are multiple random variables in the problem then correlation functions of the ''same'' random variable are also sometimes called autocorrelation. The autocorrelation can be intuitively understood as an indicator of how the random variable at a given point changes with time. Correlation functions of different random variables are sometimes called '''cross correlations'''. Cross correlations are a useful indicator of the dependencies among different random variables as a function of time.
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