Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the density of the winding number of planar Brownian motion   We obtain a formula for the density of the winding number of planar Brownian
motion around the origin, and deduce from it asymptotic expansions in inverse
powers of the logarithm of the squared time, explicit in the angular variable.
In particular, we obtain the corrections of any order to the Spitzer's law, and
also to a local limit theorem for the windings.

25
The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: solv-int
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an