The Poisson Voronoi tessellation in hyperbolic space

Jeudi 8 octobre 2015 14:00-15:00 - Elliot Paquette - Weizmann Institute, Israël

Résumé : We consider the hyperbolic Poisson Voronoi (HPV) tessellation, a tiling of hyperbolic space whose vertices are given by a homogeneous Poisson point process. These tilings are not quasi-isometric to hyperbolic space, as arbitrarily large tiles and arbitrarily small tiles may appear. Nevertheless, we show that they have « anchored expansion, » a relaxation of non-amenability. Due to symmetries of hyperbolic space, the dual graph of HPV is an example of a unimodular random graph. This, together with anchored expansion, allows us to conclude many properties of HPV, such as its having positive speed and an infinite dimensional Poisson boundary.
This is based on joint works with Itai Benjamini, Yoav Krauz, and Josh Pfeffer.

Lieu : Salle 117-119

The Poisson Voronoi tessellation in hyperbolic space  Version PDF