Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variance expansion and Berry-Esseen bound for the number of vertices of
  a random polygon in a polygon   Fix a container polygon $P$ in the plane and consider the convex hull $P_n$
of $n\geq 3$ independent and uniformly distributed in $P$ random points. In the
focus of this paper is the vertex number of the random polygon $P_n$. The
precise variance expansion for the vertex number is determined up to the
constant-order term, a result which can be considered as a second-order
analogue of the classical expansion for the expectation of R\'enyi and Sulanke
(1963). Moreover, a sharp Berry-Esseen bound is derived for the vertex number
of the random polygon $P_n$, which is of the same order as the square-root of
the variance. The main idea behind the proof of both results is a decomposition
of the boundary of the random polygon $P_n$ into random convex chains and a
careful merging of the variance expansions and Berry-Esseen bounds for the
vertex numbers of the individual chains.

3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga