Cross-correlation matrix: Difference between revisions

Revision as of 02:20, 17 September 2015

Revision as of 19:37, 22 July 2016

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:<math>C_{i_1i_2\cdots i_n}(s_1,s_2,\cdots,s_n) = \langle X_{i_1}(s_1) X_{i_2}(s_2) \cdots X_{i_n}(s_n)\rangle.</math>

If the random variable has only one component, then the indices <math>i_ji,j</math> are redundant. If there are symmetries, then the correlation function can be broken up into [[irreducible representation]]s of the symmetries &mdash; both internal and spacetime.

The case of correlations of a single random variable can be thought of as a special case of autocorrelation of a stochastic process on a space which contains a single point.