Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance statistics in random media: high dimension and/or high
  neighborhood order cases   Consider an unlimited homogeneous medium disturbed by points generated via
Poisson process. The neighborhood of a point plays an important role in spatial
statistics problems. Here, we obtain analytically the distance statistics to
$k$th nearest neighbor in a $d$-dimensional media. Next, we focus our attention
in high dimensionality and high neighborhood order limits. High dimensionality
makes distance distribution behavior as a delta sequence, with mean value equal
to Cerf's conjecture. Distance statistics in high neighborhood order converges
to a Gaussian distribution. The general distance statistics can be applied to
detect departures from Poissonian point distribution hypotheses as proposed by
Thompson and generalized here.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
2
The categories of this paper are: math
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex