Tales of Random Projections of High-dimensional Measures
Properties of random projections of high-dimensional probability measures are of interest in a variety of fields, including asymptotic convex geometry, and high-dimensional statistics and data analysis. A particular question of interest is to identify what properties of the high-dimensional measure are captured by its lower-dimensional projections. While fluctuations of these projections have been well studied over the past decade, we describe more recent work on large deviations principles and associated conditional limit theorems for (possibly multidimensional) projections. This talk is based on joint works with Nina Gantert, Steven Kim and Yin-Ting Liao.