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Long-range correlation: Difference between revisions
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However, often it is observed that the correlation exhibits a slower decay for large values of the delay (or distance) Δ, namely an algebraic decay proportional to 1/Δ<sup>α</sup> (α > 0 but not too large, < 2). | However, often it is observed that the correlation exhibits a slower decay for large values of the delay (or distance) Δ, namely an algebraic decay proportional to 1/Δ<sup>α</sup> (α > 0 but not too large, < 2). | ||
In this case, the correlations at large delay may be quite important to understand the global system behaviour (contrasting sharply with the exponential decay case). | In this case, the correlations at large delay may be quite important to understand the global system behaviour (contrasting sharply with the exponential decay case). | ||
The particular choice of the power law as the main alternative of the exponential decay is not casual: it is motivated by the fact that [[:Wikipedia:Power law|power law distributions are self-similar]]. | |||
Particularly, an algebraic decay of the mentioned type implies that no particular ''scale length'' can be assigned to the turbulent dynamics, and all scales (up to the system size) will participate in the global description of system behaviour. | Particularly, an algebraic decay of the mentioned type implies that no particular ''scale length'' can be assigned to the turbulent dynamics, and all scales (up to the system size) will participate in the global description of system behaviour. | ||