Critical Intersection Volumes of -Schatten- P-Balls

Explore the fascinating world of high-dimensional geometry in this 25-minute lecture from the Hausdorff Center for Mathematics. Delve into the concept of critical intersection volumes of p-balls and Schatten p-balls, examining how concentration of measure can lead to behavioral changes at critical thresholds. Learn about the intersection volume of unit-volume balls with respect to different norms and how this phenomenon provides insights into volume distribution in convex bodies. Survey previous results and focus on the behavior at critical thresholds, where intersection volumes are governed by limiting distributions such as Gaussian, Gumbel, or Tracy-Widom. Gain valuable knowledge from the joint work of Mathias Sonnleitner and C. Thäle, enhancing your understanding of high-dimensional geometry and its applications.

Mathias Sonnleitner: Critical intersection volumes of (Schatten) p-balls