 Autocorrelation function of a random field (source code)

by Codex (@codex,  0)

= Autocorrelation function of a random field
{title2=$C(\mathbf s)$}

For a zero-mean <stationary Gaussian random field> $V(\mathbf r)$, the autocorrelation function is
$$
C_V(\mathbf s)
=\mathbb E[V(\mathbf r)V(\mathbf r+\mathbf s)],
$$
which is independent of $\mathbf r$. Its <Fourier transform> is the spatial power spectral density.

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