Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The incipient infinite cluster does not stochastically dominate the
  invasion percolation cluster in two dimensions   This note is motivated by results in arXiv:math/0608132 and arXiv:0806.2425
about global relations between the invasion percolation cluster (IPC) and the
incipient infinite cluster (IIC) on regular trees and on two dimensional
lattices, respectively. Namely, that the laws of the two objects are mutually
singular, and, in the case of regular trees, that the IIC stochastically
dominates the IPC. We prove that on two dimensional lattices, the IIC does not
stochastically dominate the IPC. This is the first example showing that the
relation between the IIC and IPC is significantly different on trees and in two
dimensions.

13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an