Kinetic limits for pair-interaction driven master equations and biological swarm models (Q2836500)

In this paper, the passage from stochastic particle systems to kinetic equations is considered in the case where the number of particles tends to infinity. In particular, the authors are interested in a class of processes which are inspired by biological swarm models. Starting with the master equation that describes the evolution of the \(N\)-particle probability distribution of the system, the master equation is then posed on a large-dimensional space consisting of an \(N\)-fold copy of the single-particle phase space. In the spatially homogeneous case, a propagation of the chaos result is established for this class of master equations; it generalizes a well-known result for the Kac model in kinetic theory. This result is applied then for the analysis of kinetic limits for two biological swarm models, the BDG (Bertin-Droz-Grégoire) and CL (Choose the Leader) processes. It has been shown that propagation of chaos may be lost at large times. An example where the invariant density is not chaotic is provided for the CL process.