Stationary Gaussian random field

A stationary Gaussian random field has Gaussian finite-dimensional distributions invariant under common spatial translations. Its mean is constant and its two-point covariance depends only on the separation of the points.

For a zero-mean stationary Gaussian random field $V(\mathbf{r})$, the autocorrelation function iswhich is independent of $\mathbf{r}$. Its Fourier transform is the spatial power spectral density.