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There is another reason, although it is not intuitive. A stochastic process is almost completely characterised by its auto-correlation function. More precisely, if the process is stationary (of course, all these methods only work after a process has been de-trended and all cycles analysed and filtered out first) and Gaussian, and centred, then it is ...

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You are right, there is no relation. And your intuition gives one way to see why. If you take an average function f and convolve it with a nice, smooth, function g, this smooths f more but also spreads it out more: the smoothness becomes better, but the support of f, the domain where it is non-zero, becomes "worse", so to speak. So the convolution is ...

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Veneziano amplitude is a 4 tachyon amplitude in bosonic open string theory. Two tachyons are ingoing and two are outgoing. From the stringy point of view, tachyons are present in both closed and open bosonic theory and are the lowest particle in the spectrum, in particular they have negative mass squared: $m_\textrm{open}^2=\frac{-1}{\alpha'}$. In general a ...

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In statistical mechanics and field theory, the second type is referred to as a "connected" correlation function. You sometimes see the notation $$g_{\text{c}}(\mathbf{x}-\mathbf{x'},t-t') = \langle s_1(\mathbf{x},t) s_2(\mathbf{x}',t') \rangle_{\text{c}}\,\text{,}$$ where $\langle\ldots\rangle_{\text{c}}$ indicates that the product of the averages should ...

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The second version is the first one but with the observables shifted by their respective averages: $$\langle \tilde A\tilde B\rangle = \langle (A-\langle A\rangle)(B-\langle B\rangle)\rangle = \langle AB\rangle - \langle A\rangle\langle B\rangle$$ Oftentimes in e.g. numerical studies, it is easier to just sample the average product of the original ...

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The general Pearson correlation between two variables is defined as $$\textrm{cor}(X,Y) = E[XY] - E[X]E[Y]$$ up to a denominator containing the standard deviations of the distributions of the two variables. In some field theories the expectation values of the variable itself (one-point function) vanishes, therefore oftentimes the above definition reduces ...

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Think of experiments where a particle interferes with itself, like in the double slit. The coherence function tells you if one part of the wavefunction is capable of interfering with another part. For example, if the part exiting the left slit can interfere with the one on the right. If something (like a detector, or bumping into stuff) adds random phase to ...

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