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arXiv · 2005.04911

Limit theorems for random points in a simplex

Anastas Baci·Zakhar Kabluchko·Joscha Prochno·Mathias Sonnleitner·Christoph Thaele
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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 $q=\infty$. A comparison with corresponding results for $\ell_p^n$-balls is carried out as well.

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Anastas Baci, Zakhar Kabluchko, Joscha Prochno, Mathias Sonnleitner, Christoph Thaele. 2020-05-11. Limit theorems for random points in a simplex. https://arxiv.org/abs/2005.04911

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