# 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}
}
• Published 23 February 2022
• Physics
• Kinetic and Related Models
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

## Figures from this paper

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

• Mathematics
• 2022
In this article we wish to show, in a concise manner, a result of uniform in time propagation of chaos on random graphs. To do so, we combine the approaches of Delattre, Giacomin and Luc¸on [12] and

### Importance Sampling for the Empirical Measure of Weakly Interacting Diffusions

• Mathematics
• 2022
. We construct an importance sampling method for computing statistics related to rare events for weakly interacting diﬀusions. Standard Monte Carlo methods behave exponentially poorly with the number

• 2022

### Strong and weak convergence for averaging principle of DDSDE with singular drift

• Mathematics
• 2022
In this paper, we study the averaging principle for distribution dependent stochastic diﬀerential equations with drift in localized L p spaces. Using Zvonkin’s transformation and estimates for

### Nonlinear recombinations and generalized random transpositions

• Mathematics
• 2022
. We study a nonlinear recombination model from population genetics as a combinatorial version of the Kac-Boltzmann equation from kinetic theory. Following Kac’s approach, the nonlinear model is

### Global contractivity for Langevin dynamics with distribution-dependent forces and uniform in time propagation of chaos

. 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, Mathematics
ArXiv
• 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 Science
ArXiv
• 2022
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.

## References

SHOWING 1-10 OF 81 REFERENCES

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

• Materials Science
Probability 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

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

• Mathematics
Communications 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

• Samir Salem
• Mathematics
Discrete & Continuous Dynamical Systems - A
• 2020

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

• Physics, Mathematics
Stochastic 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