High-dimensional limit theorems for random vectors in ${\ell }_p^n$-balls

Zakhar Kabluchko, Joscha Prochno, Christoph Thaele

In this paper, we prove a multivariate central limit theorem for ${\ell }_q$-norms of high-dimensional random vectors that are chosen uniformly at random in an ${\ell }_p^n$-ball. As a c…