David Steigenberger: Random Beta Simplices and Parallelotopes

Explore the mathematical concepts of random simplices and parallelotopes in this 23-minute lecture from the Hausdorff Center for Mathematics. Delve into the study of convex hulls and Minkowski sums of independent, non-identically distributed random vectors in R^d. Examine beta-distributed vectors with varying parameters and their special cases, including uniform distributions on unit balls and spheres, as well as Gaussian distributions. Learn about an explicit formula for the expected volume of beta simplices, derived through a geometric approach connecting simplex and parallelotope volumes. Discover how this formula leads to a distributional representation of beta simplex volumes, reinforcing the geometrical relationship. Gain insights from the joint work of David Steigenberger, Zakhar Kabluchko, and Christoph Thäle in this advanced mathematical exploration.