Boolean Models in Hyperbolic Space

Explore the fascinating world of Boolean models in hyperbolic space through this 49-minute lecture by Daniel Hug at the Hausdorff Center for Mathematics. Delve into the study of stationary Poisson processes of compact (convex) sets in hyperbolic space, comparing and contrasting with classical Euclidean models. Examine geometric functionals, such as the volume of intersections with compact convex observation windows, and investigate their asymptotic behavior for balls with increasing radii. Discover exact and asymptotic formulas for expectation, variances, and covariances, as well as univariate and multivariate central limit theorems. Gain insights into the unique phenomena that emerge in hyperbolic space, offering a fresh perspective on this advanced topic in stochastic geometry.