Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic evolution of a continuum particle system with dispersal and
  competition: micro- and mesoscopic description   A Markov evolution of a system of point particles in $\mathbb{R}^d$ is
described at micro-and mesoscopic levels. The particles reproduce themselves at
distant points (dispersal) and die, independently and under the influence of
each other (competition). The microscopic description is based on an infinite
chain of equations for correlation functions, similar to the BBGKY hierarchy
used in the Hamiltonian dynamics of continuum particle systems. The mesoscopic
description is based on a Vlasov-type kinetic equation for the particle's
density obtained from the mentioned chain via a scaling procedure. The main
conclusion of the microscopic theory is that the competition can prevent the
system from clustering, which makes its description in terms of densities
reasonable. A possible homogenization of the solutions to the kinetic equation
in the long-time limit is also discussed.

10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
13
The categories of this paper are: quant-ph