A conditional limit theorem for high-dimensional ℓᵖ-spheres. (16th January 2019) - Kim, Steven S.; Ramanan, Kavitar
Abstract: The study of high-dimensional distributions is of interest in probability theory, statistics, and asymptotic convex geometry, where the object of interest is the uniform distribution on a convex set in high dimensions. The ℓ p -spaces and norms are of particular interest in this setting. In this paper we establish a limit theorem for distributions on ℓ p -spheres, conditioned on a rare event, in a high-dimensional geometric setting. As part of our proof, we establish a certain large deviation principle that is also relevant to the study of the tail behavior of random projections of ℓ p -balls in a high-dimensional Euclidean space.