Covariance of a squared random field
= Covariance of a squared random field
{title2=$\operatorname{Cov}(n^2,n'^2)$}
For $W=n^2-\langle n^2\rangle$, the <covariance function> is $\langle n^2n'^2\rangle-\langle n^2\rangle\langle n'^2\rangle$. It involves fourth moments and is not determined by the two-point correlation of $n$ in general. For a centered Gaussian pair the fourth-moment identity reduces it to $2\langle nn'\rangle^2$. This extra Gaussian hypothesis must be stated before using that reduction.