Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Percolation of random nodal lines   We prove a Russo-Seymour-Welsch percolation theorem for nodal domains and
nodal lines associated to a natural infinite dimensional space of real analytic
functions on the real plane. More precisely, let $U$ be a smooth connected
bounded open set in $\mathbb R^2$ and $\gamma, \gamma'$ two disjoint arcs of
positive length in the boundary of $U$. We prove that there exists a positive
constant $c$, such that for any positive scale $s$, with probability at least
$c$ there exists a connected component of $\{x\in \bar U, \, f(sx)
\textgreater{} 0\} $ intersecting both $\gamma$ and $\gamma'$, where $f$ is a
random analytic function in the Wiener space associated to the real
Bargmann-Fock space. For $s$ large enough, the same conclusion holds for the
zero set $\{x\in \bar U, \, f(sx) = 0\} $. As an important intermediate result,
we prove that sign percolation for a general stationary Gaussian field can be
made equivalent to a correlated percolation model on a lattice.

25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int