Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multivariate normal approximation in geometric probability   Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is
over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded
region in $d$-space, and $\xi_x$ is a functional determined by the Poisson
points near to $x$, i.e. satisfying an exponential stabilization condition,
along with a moments condition (examples include statistics for proximity
graphs, germ-grain models and random sequential deposition models). A known
general result says the $\mu_\lambda$-measures (suitably scaled and centred) of
disjoint sets in $R^d$ are asymptotically independent normals as $\lambda \to
\infty$; here we give an $O(\lambda^{-1/(2d + \epsilon)})$ bound on the rate of
convergence. We illustrate our result with an explicit multivariate central
limit theorem for the nearest-neighbour graph on Poisson points on a finite
collection of disjoint intervals.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga