Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Asymptotic Number of Plane Curves and Alternating Knots   We present a conjecture for the power-law exponent in the asymptotic number
of types of plane curves as the number of self-intersections goes to infinity.
In view of the description of prime alternating links as flype equivalence
classes of plane curves, a similar conjecture is made for the asymptotic number
of prime alternating knots. The rationale leading to these conjectures is given
by quantum field theory. Plane curves are viewed as configurations of loops on
a random planar lattices, that are in turn interpreted as a model of 2d quantum
gravity with matter. The identification of the universality class of this model
yields the conjecture. Since approximate counting or sampling planar curves
with more than a few dozens of intersections is an open problem, direct
confrontation with numerical data yields no convincing indication on the
correctness of our conjectures. However, our physical approach yields a more
general conjecture about connected systems of curves. We take advantage of this
to design an original and feasible numerical test, based on recent perfect
samplers for large planar maps. The numerical datas strongly support our
identification with a conformal field theory recently described by Read and
Saleur.

13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga