Published online by Cambridge University Press: 21 June 2022
In this work the
$\ell_q$
-norms of points chosen uniformly at random in a centered regular simplex in high dimensions are studied. Berry–Esseen bounds in the regime
$1\leq q < \infty$
are derived and complemented by a non-central limit theorem together with moderate and large deviations in the case where
$q=\infty$
. An application to the intersection volume of a regular simplex with an
$\ell_p^n$
-ball is also carried out.