Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dependent Double Branching Annihilating Random Walk   Double (or parity conserving) branching annihilating random walk, introduced
by Sudbury in '90, is a one-dimensional non-attractive particle system in which
positive and negative particles perform nearest neighbor hopping, produce two
offsprings to neighboring lattice points and annihilate when they meet. Given
an odd number of initial particles, positive recurrence as seen from the
leftmost particle position was first proved by Belitsky, Ferrari, Menshikov and
Popov in '01 and, subsequently in a much more general setup, in the article by
Sturm and Swart (Tightness of voter model interfaces) in '08. These results
assume that jump rates of the various moves do not depend on the configuration
of the particles not involved in these moves. The present article deals with
the case when the jump rates are affected by the locations of several particles
in the system. Motivation for such models comes from non-attractive interacting
particle systems with particle conservation. Under suitable assumptions we
establish the existence of the process, and prove that the one-particle state
is positive recurrent. We achieve this by arguments similar to those appeared
in the previous article by Sturm and Swart. We also extend our results to some
cases of long range jumps, when branching can also occur to non-neighboring
sites. We outline and discuss several particular examples of models where our
results apply.

10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci