  Disordered stealthy many-particle systems in $\mathbb{R}^d$ are exotic states
of matter that suppress single scattering events for a finite range of
wavenumbers around the origin in reciprocal space. We derive analytical
formulas for the nearest-neighbor functions of disordered stealthy systems.
First, we analyze asymptotic small-$r$ approximations and bounding expressions
of the nearest-neighbor functions based on the pseudo-hard-sphere ansatz. We
then determine how many of the standard $n$-point correlation functions are
needed to determine the nearest neighbor functions, and find that a finite
number suffice. Via theoretical and computational methods, we compare the
large-$r$ behavior of these functions for disordered stealthy systems to those
belonging to crystalline lattices. Such ordered and disordered stealthy systems
have bounded hole sizes. However, we find that the approach to the
critical-hole size can be quantitatively different. We argue that the
probability of finding a hole close to the critical-hole size should decrease
as a power law with an exponent only dependent on the space dimension $d$ for
ordered systems, but that this probability decays asymptotically faster for
disordered systems. This implies that holes close to the critical-hole size are
rarer in disordered systems. The rarity of observing large holes in disordered
systems creates substantial numerical difficulties in sampling the nearest
neighbor distributions near the critical-hole size. This motivates both the
need for new computational methods for efficient sampling and the development
of novel theoretical methods. We also devise a simple analytical formula that
accurately describes these systems in the underconstrained regime for all $r$.
These results provide a foundation for the analytical description of the
nearest-neighbor functions of stealthy systems in the disordered,
underconstrained regime.
