Conditional pair distributions in many-body systems: Exact results for
  Poisson ensembles
  We introduce a conditional pair distribution function (CPDF) which
characterizes the probability density of finding an object (e.g., a particle in
a fluid) to certain distance of other, with each of these two having a nearest
neighbor to a fixed but otherwise arbitrary distance. This function describes
special four-body configurations, but also contains contributions due to the
so-called mutual nearest neighbor (two-body) and shared neighbor (three-body)
configurations. The CPDF is introduced to improve a Helmholtz free energy
method based on space partitions. We derive exact expressions of the CPDF and
various associated quantities for randomly distributed, non-interacting points
at Euclidean spaces of one, two and three dimensions. Results may be of
interest in many diverse scientific fields, from fluid physics to social and
biological sciences.
