Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inhomogeneous percolation on ladder graphs   We define an inhomogeneous percolation model on "ladder graphs" obtained as
direct products of an arbitrary graph $G = (V,E)$ and the set of integers
$\mathbb{Z}$ (vertices are thought of as having a "vertical" component indexed
by an integer). We make two natural choices for the set of edges, producing an
unoriented graph $\mathbb{G}$ and an oriented graph $\vec{\mathbb{G}}$. These
graphs are endowed with percolation configurations in which independently,
edges inside a fixed infinite "column" are open with probability $q$, and all
other edges are open with probability $p$. For all fixed $q$ one can define the
critical percolation threshold $p_c(q)$. We show that this function is
continuous in $(0, 1)$.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex