Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharpness of the Phase Transition for the Orthant Model   The orthant model is a directed percolation model on $\mathbb{Z}^d$, in which
all clusters are infinite. We prove a sharp threshold result for this model: if
$p$ is larger than the critical value above which the cluster of $0$ is
contained in a cone, then the shift from $0$ that is required to contain the
cluster of $0$ in that cone is exponentially small. As a consequence, above
this critical threshold, a shape theorem holds for the cluster of $0$, as well
as ballisiticity of the random walk on this cluster.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph