Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Crossing probabilities for planar percolation   We prove a general Russo-Seymour-Welsh result valid for any invariant planar
percolation process satisfying positive association. This means that the
probability of crossing a rectangle in the long direction is related by a
homeomorphism to the probability of crossing it in the short direction. This
homeomorphism is universal in the sense that it depends only on the aspect
ratio of the rectangle, and is uniform in the scale and the considered model.

10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys