Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Branching diffusion with interactions   A $d$-dimensional branching diffusion, $Z$, is investigated, where the linear
attraction or repulsion between particles is competing with an
Ornstein-Uhlenbeck drift, with parameter $b$ (we take $b>0$ for inward O-U and
$b<0$ for outward O-U). This work has been motivated by [4], where a similar
model was studied, but without the drift component.
  We show that the large time behavior of the system depends on the interaction
and the drift in a nontrivial way. Our method provides, inter alia, the SLLN
for the non-interactive branching (inward) O-U process.
  First, regardless of attraction ($\gamma >0$) or repulsion ($\gamma <0$),
a.s., as time tends to infinity, the center of mass of $Z$
  (i) converges to the origin, when $b>0$;
  (ii) escapes to infinity exponentially fast (rate $|b|$), when $b<0$.
  We then analyze $Z$ as viewed from the center of mass, and finally, for the
system as a whole, we show a number of results/conjectures regarding the long
term behavior of the system; some of these are scaling limits, while some
others concern local extinction.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio