Collective phenomena in interacting particle systems (Q580830)

One considers a class of stochastic interacting particle systems for which the generator splits into two parts, one ``much larger'' than the other. As a consequence two time scales arise: for short times the system is ruled by the larger (diffusive) part of the generator, for longer time scales the effect of the second (birth-death) part is felt. In the (kinetic) continuum limit, analogous to the Boltzmann-Grad limit, we prove propagation of chaos and convergence of the density field to the solution of a partial differential equation of the reaction-diffusion type.