Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Active spanning trees and Schramm-Loewner evolution   We consider the Peano curve separating a spanning tree from its dual spanning
tree on an embedded planar graph, where the tree and dual tree are weighted by
$y$ to the number of active edges, and "active" is in the sense of the Tutte
polynomial. When the graph is a portion of the square grid approximating a
simply connected domain, it is known ($y=1$ and $y=1+\sqrt{2}$) or believed
($1<y<3$) that the Peano curve converges to a space-filling SLE$_{\kappa}$
loop, where $y=1-2\cos(4\pi/\kappa)$, corresponding to $4<\kappa\leq 8$. We
argue that the same should hold for $0\le y<1$, which corresponds to
$8<\kappa\leq 12$.

0
The categories of this paper are: hep-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
18
The categories of this paper are: econ
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin