Riv. Mat. Univ. Parma, Vol. 3, No. 2, 2012

Bernt Wennberg

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

Pages: 291-344
Received: 14 February 2011   
Accepted: 21 March 2011
Mathematics Subject Classification (2010): 92D15, 92D50, 82C40, 60J25, 60J75.

Keywords: Interacting particle systems, master equation, propagation of chaos, Boltzmann equation, speciation, adaptive dynamics.

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Abstract: The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles goes 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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