Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the fractal structure of the universe: methods, results and
  theoretical implication   The fact that galaxy distribution exhibits fractal properties is well
established since twenty years. Nowadays, the controversy concerns the range of
the fractal regime, the value of the fractal dimension and the eventual
presence of a cross-over to homogeneity. Fractal properties maybe studied with
methods which do not assume homogeneity a priori as the standard statistical
methods do. We show that complementary to the adoption of new methods of
analysis there are important theoretical implications for the usual scenario of
galaxy formation. For example, we focus on the concept of bias and we show that
it needs a basic revision even if future redshift surveys will be able to
identify an eventual tendency to homogenization.

31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org