Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Variance of the Area of Planar Cylinder Processes Driven by
  Brillinger-Mixing Point Processes   We study some asymptotic properties of cylinder processes in the plane
defined as union sets of dilated straight lines (appearing as mutually
overlapping infinitely long strips) derived from a stationary independently
marked point process on the real line, where the marks describe thickness and
orientation of individual cylinders. Such cylinder processes form an important
class of (in general non-stationary) planar random sets. We observe the
cylinder process in an unboundedly growing domain $\rho K$ when $\rho \to
\infty\,$, where the set $K$ is compact and star-shaped w.r.t. the origin ${\bf
o}$ being an inner point of $K$. Provided the unmarked point process satisfies
a Brillinger-type mixing condition and the thickness of the typical cylinder
has a finite second moment we prove a (weak) law of large numbers as well as a
formula of the asymptotic variance for the area of the cylinder process in
$\rho K$. Due to the long-range dependencies of the cylinder process, this
variance increases proportionally to $\rho^3$.

18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph