Central limit theorems for random polytopes in a smooth convex set

Van Vu

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Central limit theorems for random polytopes in a smooth convex set

Van Vu

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Abstract

Let $K$ be a smooth convex set with volume one in $\BBR^d$. Choose $n$ random points in $K$ independently according to the uniform distribution. The convex hull of these points, denoted by $K_n$, is called a {\it random polytope}. We prove that several key functionals of $K_n$ satisfy the central limit theorem as $n$ tends to infinity.

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Van Vu. 2005-03-24. Central limit theorems for random polytopes in a smooth convex set. https://arxiv.org/abs/math/0503559

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