Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Monotonicity of escape probabilities for branching random walks on
  \Z^{d}   We study nearest-neighbors branching random walks started from a point at the
interior of a hypercube. We show that the probability that the process escapes
the hypercube is monotonically decreasing with respect to the distance of its
starting point from the boundary. We derive as a consequence that at all times
the number of particles at a site is monotonically decreasing with respect to
its distance from the starting point.

18
The categories of this paper are: econ
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat