  We study spatial correlations of vortices in different quantum states or with
Bose or Fermi statistics. This is relevant for both optical vortices and
condensed-matter ones such as microcavity polaritons, or any platform that can
prepare and image fields in space at the few-particle level. While we focus on
this particular case for illustration of the formalism, we already reveal
unexpected features of spatial condensation whereby bosons exhibit a bimodal
distribution of their distances which places them farther apart than fermions
in over 40% of the cases, or on the opposite conceal spatial correlations to
behave like coherent states. Such experiments upgrade in the laboratory
successful techniques in uncontrolled extreme environments (stars and nuclei).
