Anchored expansion of Delaunay complexes in real hyperbolic space and stationary point processes

We give sufficient conditions for a discrete set of points in any dimensional real hyperbolic space to have positive anchored expansion. The first condition is an bounded density property, ensuring not too many can accumulate large regions. second vacancy condition, effectively there much left vacant by the over These properties as easy corollary that stationary Poisson–Delaunay graphs expansion, well Delaunay built from determinantal point processes.