Pierre Calka- Close-Up on Random Convex Hulls

Explore the fascinating world of random convex hulls in this 28-minute lecture from the Hausdorff Center for Mathematics. Delve into the study of convex hulls formed by random points uniformly distributed within smooth convex bodies. Examine the asymptotic behavior of the Hausdorff distance between random polytopes and initial smooth convex bodies as the input size approaches infinity. Learn about the convergence to the Gumbel distribution and the calculation of the extremal index. Discover how the problem can be reinterpreted in the case of a unit ball as a covering probability of the unit sphere by spherical caps. Gain insights into the application of these techniques in high-dimensional contexts. Based on collaborative research with Joe Yukich and Benjamin Dadoun, this talk offers a deep dive into the mathematics of random convex structures.