Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of random measures in geometric probability   Given $n$ independent random marked $d$-vectors $X_i$ with a common density,
define the measure $\nu_n = \sum_i \xi_i $, where $\xi_i$ is a measure (not
necessarily a point measure) determined by the (suitably rescaled) set of
points near $X_i$. Technically, this means here that $\xi_i$ stabilizes with a
suitable power-law decay of the tail of the radius of stabilization. For
bounded test functions $f$ on $R^d$, we give a law of large numbers and central
limit theorem for $\nu_n(f)$. The latter implies weak convergence of
$\nu_n(\cdot)$, suitably scaled and centred, to a Gaussian field acting on
bounded test functions. The general result is illustrated with applications
including the volume and surface measure of germ-grain models with unbounded
grain sizes.

8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex