Central limit theorems for random polytopes in a smooth convex set

Details Central limit theorems for random polytopes in a smooth convex set Central limit theorems for random polytopes in a smooth convex set

2005-03-24

arxiv.org/abs/math/0503559v1

Mathematics

Probability

23 pages, no figure

Scientific paper

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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