Hyperuniform point sets on projective spaces

Abstract

We extend the notion of hyperuniformity to the projective spaces ${\mathbb{RP}}^{d-1}$, ${\mathbb{CP}}^{d-1}$, ${\mathbb{HP}}^{d-1}$, and ${\mathbb{OP}}^2$. We show that hyperuniformity implies uniform distribution and present examples of deterministic point sets as well as point processes which exhibit hyperuniform behaviour.