Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The mean width of random polytopes circumscribed around a convex body   Let K be a d-dimensional convex body, and let $K^{(n)}$ be the intersection
of n halfspaces containing $K$ whose bounding hyperplanes are independent and
identically distributed. Under suitable distributional assumptions, we prove an
asymptotic formula for the expectation of the difference of the mean widths of
$K^{(n)}$ and K, and another asymptotic formula for the expectation of the
number of facets of $K^{(n)}$. These results are achieved by establishing an
asymptotic result on weighted volume approximation of $K$ and by "dualizing" it
using polarity.

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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: math-ph