Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: To fixate or not to fixate in two-type annihilating branching random
  walks   We study a model of competition between two types evolving as branching
random walks on $\mathbb{Z}^d$. The two types are represented by red and blue
balls respectively, with the rule that balls of different colour annihilate
upon contact. We consider initial configurations in which the sites of
$\mathbb{Z}^d$ contain one ball each, which are independently coloured red with
probability $p$ and blue otherwise. We address the question of \emph{fixation},
referring to the sites eventually settling for a given colour, or not. Under a
mild moment condition on the branching rule, we prove that the process will
fixate almost surely for $p\neq 1/2$, and that every site will change colour
infinitely often almost surely for the balanced initial condition $p=1/2$.

36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
19
The categories of this paper are: eess
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th