Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mean Distance to the n-th Neighbour in a Uniform Distribution of
  Random Points: An Application of Probability Theory   We study different ways of determining the mean distance $ < r_n >$ between a
reference point and its $n$-th neighbour among random points distributed with
uniform density in a $D$-dimensional Euclidean space. First we present a
heuristic method; though this method provides only a crude mathematical result,
it shows a simple way of estimating $ < r_n >$. Next we describe two
alternative means of deriving the exact expression of $<r_n>$: we review the
method using absolute probability and develop an alternative method using
conditional probability. Finally we obtain an approximation to $ < r_n >$ from
the mean volume between the reference point and its $n$-th neighbour and
compare it with the heuristic and exact results.

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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
19
The categories of this paper are: eess
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The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
10
The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc