The Large Deviations Approach to High-Dimensional Convex Bodies - Lecture I

Explore the fascinating world of high-dimensional convex bodies in this 51-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 via their projections. Gain an introduction to basic concepts of large deviations theory and examine recent contributions in the field, including work by Gantert, Kim, and Ramanan. Investigate a recent result by Kim, Liao, and Ramanan on LDPs under asymptotic thin shell conditions, complementing the central limit theorem for convex sets.