Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fractal distribution of galaxies and the transition to homogeneity   There is an ongoing debate in cosmology about the value of the length scale
at which ``homogeneity'' in the matter distribution is reached or even if such
a scale exists. In the wake of this debate, we intend in this letter to clarify
the meaning of the statement transition to homogeneity and of the concept of
correlation length. We show that there are two scales each associated to the
fractal and to the homogeneous regimes of the matter distribution,
respectively. The distinction between both scales has deep consequences, for
there can be a regime which despite having small fluctuations around the
average density exhibits large clusters of galaxies.

10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
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The categories of this paper are: eess
9
The categories of this paper are: nlin
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The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
2
The categories of this paper are: math
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: funct-an