Two-point phase correlation function
= Two-point phase correlation function
{title2=$p_{ij}(x,x')=\mathbb E[\chi_i(x)\chi_j(x')]$}
The indicator correlation gives the probability of specified phases at two points. Statistical homogeneity makes it depend on separation; isotropy makes it depend only on its length. In particular $p_{11}(0)=p_1$, so the connected correlation at zero separation is $p_1-p_1^2=p_1p_2$.