Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Expected Depth of Random Real Algebraic Plane Curves   In this note we study asymptotic isotopy of random real algebraic plane
curves. More precisely, we obtain a Kac-Rice type formula that gives the
expected number of two-sided components (i.e.\ ovals) of a random real
algebraic plane curve winding around a given point. In particular, we show that
expected number of such ovals for an even degree Kostlan polynomial is
$\frac{\sqrt{d}}{2}$ and independent of the given point.

36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
11
The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an