Large Deviations 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 both annealed and quenched large deviations principles for random projections, and their refinements. This talk is based on joint works with Nina Gantert, Steven Soojin Kim and Yin-Ting Liao. Contact 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 both annealed and quenched large deviations principles for random projections, and their refinements. This talk is based on joint works with Nina Gantert, Steven Soojin Kim and Yin-Ting Liao. Contact Sayan Banerjee sayan@email.unc.edu for the zoom link