  We present a homogenization theorem for isotropically-distributed point
defects, by considering a sequence of manifolds with increasingly dense point
defects. The loci of the defects are chosen randomly according to a weighted
Poisson point process, making it a continuous version of the first passage
percolation model. We show that the sequence of manifolds converges to a smooth
Riemannian manifold, while the Levi-Civita connections converge to a non-metric
connection on the limit manifold. Thus, we obtain rigorously the emergence of a
non-metricity tensor, which was postulated in the literature to represent
continuous distribution of point defects.
