Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random ball-polyhedra and inequalities for intrinsic volumes   We prove a randomized version of the generalized Urysohn inequality relating
mean-width to the other intrinsic volumes. To do this, we introduce a
stochastic approximation procedure that sees each convex body K as the limit of
intersections of Euclidean balls of large radii and centered at randomly chosen
points. The proof depends on a new isoperimetric inequality for the intrinsic
volumes of such intersections. If the centers are i.i.d. and sampled according
to a bounded continuous distribution, then the extremizing measure is uniform
on a Euclidean ball. If one additionally assumes that the centers have i.i.d.
coordinates, then the uniform measure on a cube is the extremizer. We also
discuss connections to a randomized version of the extended isoperimetric
inequality and symmetrization techniques.

18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin