  This study is motivated by a series of recent papers that show that, if a
given deterministic sequence in the unit interval has a Poisson pair
correlation function, then the sequence is uniformly distributed. Analogous
results have been proved for point sequences on higher-dimensional tori. The
purpose of this paper is to describe a simple statistical argument that
explains this observation and furthermore permits a generalisation to bounded
Euclidean domains as well as compact Riemannian manifolds.
