Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The supercluster--void network III. The correlation function as a
  geometrical statistic   We investigate properties of the correlation function of clusters of galaxies
using geometrical models. On small scales the correlation function depends on
the shape and the size of superclusters. On large scales it describes the
geometry of the distribution of superclusters. If superclusters are distributed
randomly then the correlation function on large scales is featureless. If
superclusters and voids have a tendency to form a regular lattice then the
correlation function on large scales has quasi-regularly spaced maxima and
minima of decaying amplitude; i.e., it is oscillating. The period of
oscillations is equal to the step size of the grid of the lattice.
  We calculate the power spectrum for our models and compare the geometrical
information of the correlation function with other statistics. We find that
geometric properties (the regularity of the distribution of clusters on large
scales) are better quantified by the correlation function. We also analyse
errors in the correlation function and the power spectrum by generating random
realizations of models and finding the scatter of these realizations.

1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex