{"title":"一维奇异排斥相互作用中的粒子系统:对数和Riesz气体","authors":"A. Guillin, Pierre Le Bris, Pierre Monmarch'e","doi":"10.5802/jep.235","DOIUrl":null,"url":null,"abstract":"In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that contains the Dyson Brownian motion. We start by establishing existence and uniqueness for the Riesz gases, before proving propagation of chaos with an original approach to the problem, namely coupling with a Cauchy sequence type argument. We also give a general argument to turn a result of weak propagation of chaos into a strong and uniform in time result using the long time behavior and some bounds on moments, in particular enabling us to get a uniform in time version of the result of C\\'epa-L\\'epingle.","PeriodicalId":106406,"journal":{"name":"Journal de l’École polytechnique — Mathématiques","volume":"134 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On systems of particles in singular repulsive interaction in dimension one: log and Riesz gas\",\"authors\":\"A. Guillin, Pierre Le Bris, Pierre Monmarch'e\",\"doi\":\"10.5802/jep.235\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that contains the Dyson Brownian motion. We start by establishing existence and uniqueness for the Riesz gases, before proving propagation of chaos with an original approach to the problem, namely coupling with a Cauchy sequence type argument. We also give a general argument to turn a result of weak propagation of chaos into a strong and uniform in time result using the long time behavior and some bounds on moments, in particular enabling us to get a uniform in time version of the result of C\\\\'epa-L\\\\'epingle.\",\"PeriodicalId\":106406,\"journal\":{\"name\":\"Journal de l’École polytechnique — Mathématiques\",\"volume\":\"134 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-04-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal de l’École polytechnique — Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/jep.235\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal de l’École polytechnique — Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/jep.235","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On systems of particles in singular repulsive interaction in dimension one: log and Riesz gas
In this article, we prove the first quantitative uniform in time propagation of chaos for a class of systems of particles in singular repulsive interaction in dimension one that contains the Dyson Brownian motion. We start by establishing existence and uniqueness for the Riesz gases, before proving propagation of chaos with an original approach to the problem, namely coupling with a Cauchy sequence type argument. We also give a general argument to turn a result of weak propagation of chaos into a strong and uniform in time result using the long time behavior and some bounds on moments, in particular enabling us to get a uniform in time version of the result of C\'epa-L\'epingle.