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

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

2011-04-28

arxiv.org/abs/1104.5310v1

Mathematics

Probability

These are notes from a series of lectures given at the 5$^{th}$ Summer School on Methods and Models of Kinetic Theory, Porto E

Scientific paper

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.

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