Limit theorems for random points in a simplex

Abstract In this work the $\ell_q$ -norms of points chosen uniformly at random in a centered regular simplex high dimensions are studied. Berry–Esseen bounds regime $1\leq q < \infty$ derived and complemented by non-central limit theorem together with moderate large deviations case where $q=\infty$ . An application to intersection volume an $\ell_p^n$ -ball is also carried out.