Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Poisson percolation on the oriented square lattice   In Poisson percolation each edge becomes open after an independent
exponentially distributed time with rate that decreases in the distance from
the origin. As a sequel to our work on the square lattice, we describe the
limiting shape of the component containing the origin in the oriented case. We
show that the density of occupied sites at height $y$ in the cluster is close
to the percolation probability in the corresponding homogeneous percolation
process, and we study the fluctuations of the boundary.

10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn