Kinetic Limits for Pair-Interaction Driven Master Equations and Biological Swarm Models
Artikel i vetenskaplig tidskrift, 2013
We consider a class of stochastic processes modeling binary interactions in an N-particle system. Examples of such systems can be found in the modeling of biological swarms. They lead to the definition of a class of master equations that we call pair-interaction driven master equations. In the spatially homogeneous case, we prove a propagation of chaos result for this class of master equations which generalizes Mark Kac's well-known result for the Kac model in kinetic theory. We use this result to study kinetic limits for two biological swarm models. We show that propagation of chaos may be lost at large times and we exhibit an example where the invariant density is not chaotic.
spectral
kinetic equations
propagation of chaos
behavior
continuum-limit
boltzmann-equation
stochastic particle approximations
gap
limit
Kac's master
vacuum
binary interactions
system
global validity
3-dimensional rare-gas
mean-field
Master equation