Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The scaling limit of Poisson-driven order statistics with applications
  in geometric probability   Let $\eta_t$ be a Poisson point process of intensity $t\geq 1$ on some state
space $\Y$ and $f$ be a non-negative symmetric function on $\Y^k$ for some
$k\geq 1$. Applying $f$ to all $k$-tuples of distinct points of $\eta_t$
generates a point process $\xi_t$ on the positive real-half axis. The scaling
limit of $\xi_t$ as $t$ tends to infinity is shown to be a Poisson point
process with explicitly known intensity measure. From this, a limit theorem for
the the $m$-th smallest point of $\xi_t$ is concluded. This is strengthened by
providing a rate of convergence. The technical background includes Wiener-It\^o
chaos decompositions and the Malliavin calculus of variations on the Poisson
space as well as the Chen-Stein method for Poisson approximation. The general
result is accompanied by a number of examples from geometric probability and
stochastic geometry, such as Poisson $k$-flats, Poisson random polytopes,
random geometric graphs and random simplices. They are obtained by combining
the general limit theorem with tools from convex and integral geometry.

23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom