Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random polytopes and the wet part for arbitrary probability
  distributions   We examine how the measure and the number of vertices of the convex hull of a
random sample of $n$ points from an arbitrary probability measure in
$\mathbf{R}^d$ relates to the wet part of that measure. This extends classical
results for the uniform distribution from a convex set [B\'ar\'any and Larman
1988]. The lower bound of B\'ar\'any and Larman continues to hold in the
general setting, but the upper bound must be relaxed by a factor of $\log n$.
We show by an example that this is tight.

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The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int