M 336

The Poisson hyperplane tessellation in Euclidean space is a classical and well-studied model of Stochastic Geometry. In this talk we will consider its counterpart(s) in hyperbolic space. As it turns out, Euclidean hyperplanes have more than one analogue in hyperbolic space, corresponding, roughly speaking, to thinking of hyperplanes as either totally geodesic hypersurfaces, equidistant sets from other hyperplanes, or spheres of infinite radius. In hyperbolic space these notions give rise to a one-parametric family of hyperplane-like hypersurfaces, known collectively as lambda-geodesic hypersurfaces, for lambda between 0 and 1. We will consider the isometry-invariant Poisson process of lambda-geodesic hyperplanes, and in particular its total surface area within a growing spherical window. We will study its limit theory, and prove central and non-central limit theorems, depending on the value of lambda and the ambient dimension. Based on joint work with Z. Kabluchko and C. Thäle

Daniel Rosen

Ruhr-Universität Bochum