{"title":"卡克-斯马尔模型的强混沌传播形式","authors":"Juntao Wu, Xiao Wang, Yicheng Liu","doi":"10.1007/s00033-024-02291-y","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate a strong form of propagation of chaos for Cucker–Smale model. We obtain an explicit bound on the relative entropy in terms of the number of particles between the joint law and the tensioned law of particles, which implies the mean field limit of the Cucker–Smale model and the propagation of chaos through the strong convergence of all marginals. Our method relies mainly on the new law of large numbers for Jabin and Wang (Invent Math 214:523–591, 2018) at the exponential scale.</p>","PeriodicalId":501481,"journal":{"name":"Zeitschrift für angewandte Mathematik und Physik","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A strong form of propagation of chaos for Cucker–Smale model\",\"authors\":\"Juntao Wu, Xiao Wang, Yicheng Liu\",\"doi\":\"10.1007/s00033-024-02291-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate a strong form of propagation of chaos for Cucker–Smale model. We obtain an explicit bound on the relative entropy in terms of the number of particles between the joint law and the tensioned law of particles, which implies the mean field limit of the Cucker–Smale model and the propagation of chaos through the strong convergence of all marginals. Our method relies mainly on the new law of large numbers for Jabin and Wang (Invent Math 214:523–591, 2018) at the exponential scale.</p>\",\"PeriodicalId\":501481,\"journal\":{\"name\":\"Zeitschrift für angewandte Mathematik und Physik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift für angewandte Mathematik und Physik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s00033-024-02291-y\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift für angewandte Mathematik und Physik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s00033-024-02291-y","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A strong form of propagation of chaos for Cucker–Smale model
In this paper, we investigate a strong form of propagation of chaos for Cucker–Smale model. We obtain an explicit bound on the relative entropy in terms of the number of particles between the joint law and the tensioned law of particles, which implies the mean field limit of the Cucker–Smale model and the propagation of chaos through the strong convergence of all marginals. Our method relies mainly on the new law of large numbers for Jabin and Wang (Invent Math 214:523–591, 2018) at the exponential scale.
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