Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cardinality of collisional clusters for hard spheres at low
  density   We resume the investigation, started in arXiv:1408.6571, of the statistics of
backward clusters in a gas of $N$ hard spheres of small diameter $\varepsilon$.
A backward cluster is defined as the group of particles involved directly or
indirectly in the backwards-in-time dynamics of a given tagged sphere. We
obtain an estimate of the average cardinality of clusters with respect to the
equilibrium measure, global in time, uniform in $\varepsilon, N$ for
$\varepsilon^2 N=1$ (Boltzmann-Grad regime).

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The categories of this paper are: cmp-lg
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: physics
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio