Title: Tales of Random Projections
Speaker: Kavita Ramanan (Professor of Applied Mathematics and Chair of the Graduate Program, Brown University)
Abstract: The interplay between geometry and probability in high-dimensional spaces is a fascinating subject of active research. Classical theorems in probability theory such as the central limit theorem and Cramer’s theorem can be viewed as providing information about certain scalar projections of high-dimensional product measures. In this talk we will describe the tail behavior of random projections of general (non-product) high-dimensional measures, which are of interest in diverse fields, ranging from asymptotic convex geometry to high-dimensional statistics. Along the way, we will explain why Cramer’s theorem is atypical and describe large deviation results on the Stiefel manifold. These large deviation results serve to complement the central limit theorem for convex sets, and its extensions.