Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variance Asymptotics and Scaling Limits for Random Polytopes   Let K be a convex set in R d and let K $\lambda$ be the convex hull of a
homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When
K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$
$\infty$ for the boundary of K $\lambda$ in a vicinity of a vertex of K and we
give variance asymptotics for the volume and k-face functional of K $\lambda$,
k $\in$ {0, 1, ..., d -- 1}, resolving an open question posed in [18]. The
scaling limit of the boundary of K $\lambda$ and the variance asymptotics are
described in terms of a germ-grain model consisting of cone-like grains pinned
to the extreme points of a Poisson point process on R d--1 $\times$ R having
intensity $\sqrt$ de dh dhdv.

6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th