Title: Random polytopes: An introduction and recent developments-Part II
Speaker: Julian Grote (PhD Student, University of Bochum and Case Western Reserve University)
Abstract: Random polytopes are among the most classical and popular models considered in stochastic geometry, and their study has become a rapidly developing branch of mathematics at the borderline between geometry and probability. One reason for the increasing interest are the numerous connections and applications of random polytopes in other fields of mathematics, for example algorithmic geometry, convex geometric analysis or optimization.
In this talk two different models of random polytopes are considered. At the beginning we look at Gaussian polytopes in fixed space dimension and are interested in results for the volume of these random polytopes as the number of points tends to infinity. Secondly we look at these Gaussian polytopes from a different point of view. For a fixed number of points we let the underlying space dimension tend to infinity and ask the same question for the volume of the polytope constructed as the convex hull of the point set. Both models are again analyzed using the so called method of cumulants.