Hyperuniformity under Displacements

Kurzfassung

We introduce hyperuniformity, a property of stationary point processes on R^d that describes the suppression of large-scale density fluctuations. We give some basic examples and then study when hyperuniformity is preserved under random displacements of the points. We illustrate our results with several examples, including isotropic hyperuniform point processes that can be simulated in linear time. In two and three dimensions, we can generate samples with 10^9 points. We also discuss a notion of hyperuniformity for random graphs embedded in R^d and give an example based on a modification of the Poisson-Delaunay graph.