Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expected value of the smallest denominator in a random interval of fixed
  radius   We compute the probability mass function of the random variable which returns
the smallest denominator of a reduced fraction in a randomly chosen real
interval of radius $\delta$. As an application, we prove that the expected
value of the smallest denominator is asymptotic, as $\delta\rightarrow 0$, to
$(8\sqrt{2}/\pi^2)\delta^{-1/2}.$

5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: quant-ph
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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: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: stat