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

TL;DR

This paper studies the behavior of large-scale many-particle Markov processes, focusing on biological applications like speciation and swarming, and introduces methods for deriving mean field models from these systems.

Contribution

It provides a rigorous analysis of the limiting behavior of many-particle systems in biology and abstract models, advancing the understanding of propagation of chaos.

Findings

Models for sympatric speciation and animal swarming are developed.

Methods for deriving mean field models from many-particle systems are established.

The paper demonstrates the propagation of chaos in abstract models.

Abstract

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.