Random many-particle systems: applications from biology, and propagation of chaos in abstract models

Paper in proceeding, 2012

The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric speciation, i.e. the process in which a genetically homogeneous population is split in two or more different species sharing the same habitat, and models for swarming animals. The second part of the paper deals with abstract many particle systems and methods for rigorously deriving mean field models.