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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-02-23 DOI:10.3934/krm.2022017

L. Chaintron, A. Diez

引用次数: 36

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.

查看原文本刊更多论文

混沌的传播:模型、方法和应用综述。1、模型与方法

相互作用粒子的大系统的混沌传播的概念起源于统计物理学，最近已成为应用数学许多领域的中心概念。本文介绍了该领域的一些新、旧方法和重要成果。所考虑的模型包括McKean-Vlasov扩散、平均场跳跃模型和Boltzmann模型。本综述的第一部分是介绍随机粒子系统的建模方面和混沌传播的概念。第二部分介绍了该领域的一些重要模型的具体应用和更详细的研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.