Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incidence estimates for $\alpha$-dimensional tubes and
  $\beta$-dimensional balls in $\mathbb{R}^2$   We prove essentially sharp incidence estimates for a collection of
$\delta$-tubes and $\delta$-balls in the plane, where the $\delta$-tubes
satisfy an $\alpha$-dimensional spacing condition and the $\delta$-balls
satisfy a $\beta$-dimensional spacing condition. Our approach combines a
combinatorial argument for small $\alpha, \beta$ and a Fourier analytic
argument for large $\alpha, \beta$.

18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-th
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
22
The categories of this paper are: chao-dyn