# Propagation of chaos: A review of models, methods and applications. I. Models and methods

@article{Chaintron2022PropagationOC, title={Propagation of chaos: A review of models, methods and applications. I. Models and methods}, author={Louis-Pierre Chaintron and Antoine Diez}, journal={Kinetic and Related Models}, year={2022} }

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…

## 8 Citations

### A note on uniform in time mean-field limit in graphs

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. We study the long-time behaviour of both the classical second-order Langevin dynamics and the nonlinear second-order Langevin dynamics of McKean-Vlasov type. By a coupling approach, we establish…

### Error Analysis of Time-Discrete Random Batch Method for Interacting Particle Systems and Associated Mean-Field Limits

- Computer Science, MathematicsArXiv
- 2022

Using the triangle inequality framework, it is shown that the long-time error of the discrete random batch method is O ( √ τ + e − λt ), where τ is the time step and λ is the convergence rate which does not depend on the timestep τ or the number of particles N .

### Scalable particle-based alternatives to EM

- Computer ScienceArXiv
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Three practical particle-based alternatives to EM applicable to broad classes of models are obtained through straightforward discretizations of gradient ﬂows associated with the functional.

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