Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson hyperplane processes and approximation of convex bodies   A natural model for the approximation of a convex body $K$ in $\mathbb{R}^d$
by random polytopes is obtained as follows. Take a stationary Poisson
hyperplane process in the space, and consider the random polytope $Z_K$ defined
as the intersection of all closed halfspaces containing $K$ that are bounded by
hyperplanes of the process not intersecting $K$. If $f$ is a functional on
convex bodies, then for increasing intensities of the process, the expectation
of the difference $f(Z_K)-f(K)$ may or may not converge to zero. If it does,
then the order of convergence and possible limit relations are of interest. We
study these questions if $f$ is either the hitting functional or the mean
width.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs