“Poisson hyperplanes in hyperbolic space”
Venerdì 28 Gennaio 2022, ore 14:30 - Zoom - Christoph Thaele (University of Bochum, Germany)
In the focus of this talk are random tessellations in hyperbolic space induced by Poisson point processes on the space of hyperbolic hyperplanes (totally geodesic subspaces of co-dimension 1).
In the first part of the talk we consider the so-called k-skeleton of such tessellations and prove that, when observed in a sequence of increasing observation windows, the k-volume of the k-skeleton satisfies a central limit theorem only for dimensions 2 and 3 and that asymptotic normality fails in all higher dimensions. In the second part of the talk we determine the non-Gaussian limiting distribution for the special case k=d-1 and indicate possible generalizations.