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

Conference paper
Authors Bernt Wennberg
Published in Rivista di Matematica della Università di Parma
Volume 3
Issue 2
Pages 291-344
Publication year 2012
Published at Department of Mathematical Sciences
Pages 291-344
Language en
Keywords Interacting particle systems, master equation, propagation of chaos, Boltzmann equation, speciation, adaptive dynamics
Subject categories Mathematical Analysis, Mathematical statistics, Other Mathematics


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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