Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Zipf's law for fractal voids and a new void-finder   Voids are a prominent feature of fractal point distributions but there is no
precise definition of what is a void (except in one dimension). Here we propose
a definition of voids that uses methods of discrete stochastic geometry, in
particular, Delaunay and Voronoi tessellations, and we construct a new
algorithm to search for voids in a point set. We find and rank-order the voids
of suitable examples of fractal point sets in one and two dimensions to test
whether Zipf's power-law holds. We conclude affirmatively and, furthermore,
that the rank-ordering of voids conveys similar information to the
number-radius function, as regards the scaling regime and the transition to
homogeneity. So it is an alternative tool in the analysis of fractal point
distributions with crossover to homogeneity and, in particular, of the
distribution of galaxies.

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The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci