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Limit theorems for random points in a simplex
Published online by Cambridge University Press: 21 June 2022
Abstract
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.
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- Original Article
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- Copyright
- © The Author(s), 2022. Published by Cambridge University Press on behalf of Applied Probability Trust
References
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