are, with a certain probability controlled by the link density parameter $\LinkDens$, linked. Thus, the correlations of the link distribution reflect the correlations of the unlinked liquid, and it follows that realizations of links only acquire an appreciable statistical weight if they are compatible with some reasonably probable configuration of the unlinked liquid.

The factor $\big(\frac{\LinkDens \Volu_0}{2\PartNumb \LinkPote_0}\big)^{\LinkNumb} /\LinkNumb !$ in the Deam-Edwards distribution introduces a Poissonian character to the total number $\LinkNumb$ of links. These links are envisioned to be the product of a Poisson chemical linking process. The factor $Z_{\RealDiso}(\Volu_0)$ assures that the probability of having a given random realization of links is proportional to the statistical weight for, in the unlinked liquid state, finding the to-be-linked pairs to be co-located in the liquid state to within the shape function $\exp \big(- \vert \PartPosi_{i_e}-\PartPosi_{j_e}\vert ^2  / 2\LinkScal^2\big)$.

As a result of the Deam-Edwards distribution, the mean number of links per particle is given by $\lda \LinkNumb \rda/\PartNumb = \LinkDens/2$. Thus, $\LinkDens = 2 \lda \LinkNumb \rda/N$ is the *mean coordination number*, i.e., the average number of particles to which a certain particle is connected, [[the factor of $2$ results from the fact that each link is shared by 