Nicolas Curien: Ideal Poisson-Voronoi tiling

Описание к видео Nicolas Curien: Ideal Poisson-Voronoi tiling

We study the limit in low intensity of Poisson--Voronoi tessellations in hyperbolic spaces. In contrast to the Euclidean setting, a limiting non-trivial ideal tessellation appears as the intensity tends to 0. The tessellation obtained is a natural Möbius-invariant decomposition of the hyperbolic space into countably many infinite convex polytopes, each with a unique end. We study its basic properties, in particular the geometric features of its cells. Based on joint works with Matteo d'Achille, Nathanel Enriquez, Russell Lyons, and Meltem Unel.

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