# 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…

## 12 Citations

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### Well-posedness and propagation of chaos for L{\'e}vy-driven McKean-Vlasov SDEs under Lipschitz assumptions

- Mathematics
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- Mathematics
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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…

## References

SHOWING 1-10 OF 81 REFERENCES

### Synchronization and random long time dynamics for mean-field plane rotators

- Materials ScienceProbability Theory and Related Fields
- 2013

We consider the natural Langevin dynamics which is reversible with respect to the mean-field plane rotator (or classical spin XY) measure. It is well known that this model exhibits a phase transition…

### A λ-convexity based proof for the propagation of chaos for weakly interacting stochastic particles

- Mathematics, Computer Science
- 2020

### Long-Time Behaviors of Mean-Field Interacting Particle Systems Related to McKean–Vlasov Equations

- MathematicsCommunications in Mathematical Physics
- 2021

In this paper, we investigate concentration inequalities, exponential convergence in the Wasserstein metric W1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym}…

### A gradient flow approach of propagation of chaos

- MathematicsDiscrete & Continuous Dynamical Systems - A
- 2020

We provide an estimation of the dissipation of the Wasserstein 2 distance between the law of some interacting \begin{document}$ N $\end{document} -particle system, and the \begin{document}$ N…

### Uniform Long-Time and Propagation of Chaos Estimates for Mean Field Kinetic Particles in Non-convex Landscapes

- MathematicsJournal of Statistical Physics
- 2021

Combining the results of Guillin (Uniform Poincaré and logarithmic Sobolev inequalities for mean field particles systems, 2019) and Monmarché (Stoch Process Appl 127(6):1721–1737, 2017), the trend to…

### A consensus-based global optimization method for high dimensional machine learning problems

- Computer Science, MathematicsESAIM: Control, Optimisation and Calculus of Variations
- 2021

This work improves recently introduced consensus-based optimization method, proposed in [R. Pinnau, C. Totzeck, O. Tse, S. Martin], by replacing the isotropic geometric Brownian motion by the component-wise one, thus removing the dimensionality dependence of the drift rate, making the method more competitive for high dimensional optimization problems.

### Propagation of chaos and moderate interaction for a piecewise deterministic system of geometrically enriched particles

- Mathematics
- 2019

In this article we study a system of $N$ particles, each of them being defined by the couple of a position (in $\mathbb{R}^d$) and a so-called orientation which is an element of a compact Riemannian…

### Uniform propagation of chaos and creation of chaos for a class of nonlinear diffusions

- Physics, MathematicsStochastic Analysis and Applications
- 2019

Abstract We are interested in nonlinear diffusions in which the own law intervenes in the drift. This kind of diffusions corresponds to the hydrodynamical limit of some particle system. One also…

### On mean-field limits and quantitative estimates with a large class of singular kernels: Application to the Patlak–Keller–Segel model

- MathematicsComptes Rendus Mathematique
- 2019