Boolean Models in Hyperbolic Space

Explore Boolean models in hyperbolic space through this 26-minute lecture by Matthias Schulte from the Hausdorff Center for Mathematics. Delve into the study of isometry invariant Poisson processes on compact convex subsets of hyperbolic space, examining geometric functionals such as the volume of intersections with ball-shaped observation windows. Discover asymptotic formulas for expectations, variances, and covariances as the ball radius increases, and learn about univariate and multivariate central limit theorems. Compare these findings to the Euclidean case, noting new phenomena unique to hyperbolic space. The talk draws from joint work with Daniel Hug and Günter Last from Karlsruhe.