The Large Deviations Approach to High-Dimensional Convex Bodies, Lecture III

Explore the fascinating world of high-dimensional convex bodies in this 47-minute lecture by Joscha Prochno at the Hausdorff Center for Mathematics. Delve into the large deviations approach, which offers unique insights into the geometry of convex bodies through their lower-dimensional projections. Learn about the contrast between the universality of typical random projections and the non-universal nature of large deviation principles (LDPs). Discover how LDPs allow for distinguishing high-dimensional probability measures and their applications in convex geometry. Follow the progression from basic concepts of large deviations theory to recent developments, including the work of Kim, Liao, and Ramanan on LDPs under asymptotic thin shell conditions. Gain a deeper understanding of central limit theorems for convex sets and explore topics such as the constant regime, the alledge ball, and other key assumptions in this advanced mathematical exploration.