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Long-range correlation: Difference between revisions
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The expression 'long-range correlation' specifically refers to the slow decay of the (temporal or spatial) [[:Wikipedia:Correlation|correlation]] function (covariance), defined as | The expression 'long-range correlation' specifically refers to the slow decay of the (temporal or spatial) [[:Wikipedia:Correlation|correlation]] function (covariance), defined as | ||
<ref>[http://mathworld.wolfram.com/Cross-Correlation.html Cross-Correlation (MathWorld)]</ref> | |||
:<math>\gamma_{XY}(\Delta) = \langle X(t) Y(t+\Delta)\rangle.</math> | :<math>\gamma_{XY}(\Delta) = \langle X(t) Y(t+\Delta)\rangle.</math> | ||
Here, <math>\langle . \rangle</math> refers to an average over ''t'' and the observables ''X'' and ''Y'' depend on the time ''t'', but an analogous expression can be written down for spatial dependence. | Here, <math>\langle . \rangle</math> refers to an average over ''t'' and the observables ''X'' and ''Y'' depend on the time ''t'', but an analogous expression can be written down for spatial dependence. | ||