Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An invariance principle for branching diffusions in bounded domains   We study branching diffusions in a bounded domain $D$ of $\mathbb{R}^d$ in
which particles are killed upon hitting the boundary $\partial D$. It is known
that any such process undergoes a phase transition when the branching rate
$\beta$ exceeds a critical value: a multiple of the first eigenvalue of the
generator of the diffusion. We investigate the system at criticality and show
that the associated genealogical tree, when the process is conditioned to
survive for a long time, converges to Aldous' Continuum Random Tree under
appropriate rescaling. The result holds under only a mild assumption on the
domain, and is valid for all branching mechanisms with finite variance, and a
general class of diffusions.

12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat