Propagation of chaos: a review of models, methods and applications. II. Applications

Abstract

The notion of propagation of chaos for large systems of interacting particles originates in statistical physics and has recently become a central notion in many areas of applied mathematics. The present review describes old and new methods as well as several important results in the field. The models considered include the McKean-Vlasov diffusion, the mean-field jump models and the Boltzmann models. The first part of this review is an introduction to modelling aspects of stochastic particle systems and to the notion of propagation of chaos. The second part presents concrete applications and a more detailed study of some of the important models in the field.

190 pages. This is the second part of a two-part review article. The first part can be accessed at arXiv:2203.00446

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• Numerical methods for backward stochastic differential equations: A survey
• Consensus-Based Optimization Methods Converge Globally
• Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics
• Mean-field limits for Consensus-Based Optimization and Sampling
• Non-Stationary Critical Phenomena: Expanding The Critical Point
• A Dean-Kawasaki equation for reaction diffusion systems driven by Poisson noise
• Uniform-in-time propagation of chaos for the Cucker--Smale model
• Consensus-based algorithms for stochastic optimization problems
• Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects
• Swarm-based optimization with jumps: a kinetic BGK framework and convergence analysis
• Mean-field limit from general mixtures of experts to quantum neural networks
• Chaos propagation in genetic algorithms: An optimal transport approach
• Stochastic optimization on matrices and a graphon McKean-Vlasov limit