1 results
Limit theorems for random points in a simplex
- Part of
-
- Journal:
- Journal of Applied Probability / Volume 59 / Issue 3 / September 2022
- Published online by Cambridge University Press:
- 21 June 2022, pp. 685-701
- Print publication:
- September 2022
-
- Article
- Export citation
-
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.
