Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Direction distribution for nodal components of random band-limited
  functions on surfaces   Let $(M,g)$ be a smooth compact Riemannian surface with no boundary. Given a
smooth vector field $V$ with finitely many zeroes on $M$, we study the
distribution of the number of tangencies to $V$ of the nodal components of
random band-limited functions. It is determined that in the high-energy limit,
these obey a universal deterministic law, independent of the surface $M$ and
the vector field $V$, that is supported precisely on the even integers $2
\mathbb{Z}_{> 0}$.

25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph