  Weyl-Heisenberg ensembles are a class of determinantal point processes
associated with the Schr\"odinger representation of the Heisenberg group.
Hyperuniformity characterizes a state of matter for which (scaled) density
fluctuations diminish towards zero at the largest length scales. We will prove
that Weyl-Heisenberg ensembles are hyperuniform. Weyl-Heisenberg ensembles
include as a special case a multi-layer extension of the Ginibre ensemble
modeling the distribution of electrons in higher Landau levels, which has
recently been object of study in the realm of the Ginibre-type ensembles
associated with polyanalytic functions. In addition, the family of
Weyl-Heisenberg ensembles includes new structurally anisotropic processes,
where point-statistics depend on the different spatial directions, and thus
provide a first means to study directional hyperuniformity.
