Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Distances Associated with Hexagons   In this report, the explicit probability density functions of the random
Euclidean distances associated with regular hexagons are given, when the two
endpoints of a link are randomly distributed in the same hexagon, and two
adjacent hexagons sharing a side, respectively. Simulation results show the
accuracy of the obtained closed-form distance distribution functions, which are
important in a wide variety of applied sciences and engineering fields. In
particular, hexagons are often used in wireless communication networks such as
the cellular systems. The correctness of these distance distribution functions
is validated by a recursion and a probabilistic sum. The first two statistical
moments of the random distances, and the polynomial fits of the density
functions are also given in this report for practical uses.

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The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph