Hyperuniform Point Sets on Flat Tori: Deterministic and Probabilistic Aspects.

In this paper we study hyperuniformity on flat tori. Hyperuniform point sets on the unit sphere have been studied by J. Brauchart, P. Grabner, W. Kusner and J. Ziefle. It is shown that point sets which are hyperuniform for large balls, small balls, or balls of threshold order on the flat tori are uniformly distributed. Moreover, it is also shown that QMC-designs sequences for Sobolev classes, probabilistic point sets (obtained from jittered samplings), and some determinantal point process are hyperuniform. [ABSTRACT FROM AUTHOR]