{"title":"通过第一通道渗滤实现不可交换扩散的混沌定量传播","authors":"Daniel Lacker, Lane Chun Yeung, Fuzhong Zhou","doi":"arxiv-2409.08882","DOIUrl":null,"url":null,"abstract":"This paper develops a non-asymptotic approach to mean field approximations\nfor systems of $n$ diffusive particles interacting pairwise. The interaction\nstrengths are not identical, making the particle system non-exchangeable. The\nmarginal law of any subset of particles is compared to a suitably chosen\nproduct measure, and we find sharp relative entropy estimates between the two.\nBuilding upon prior work of the first author in the exchangeable setting, we\nuse a generalized form of the BBGKY hierarchy to derive a hierarchy of\ndifferential inequalities for the relative entropies. Our analysis of this\ncomplicated hierarchy exploits an unexpected but crucial connection with\nfirst-passage percolation, which lets us bound the marginal entropies in terms\nof expectations of functionals of this percolation process.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"212 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation\",\"authors\":\"Daniel Lacker, Lane Chun Yeung, Fuzhong Zhou\",\"doi\":\"arxiv-2409.08882\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper develops a non-asymptotic approach to mean field approximations\\nfor systems of $n$ diffusive particles interacting pairwise. The interaction\\nstrengths are not identical, making the particle system non-exchangeable. The\\nmarginal law of any subset of particles is compared to a suitably chosen\\nproduct measure, and we find sharp relative entropy estimates between the two.\\nBuilding upon prior work of the first author in the exchangeable setting, we\\nuse a generalized form of the BBGKY hierarchy to derive a hierarchy of\\ndifferential inequalities for the relative entropies. Our analysis of this\\ncomplicated hierarchy exploits an unexpected but crucial connection with\\nfirst-passage percolation, which lets us bound the marginal entropies in terms\\nof expectations of functionals of this percolation process.\",\"PeriodicalId\":501245,\"journal\":{\"name\":\"arXiv - MATH - Probability\",\"volume\":\"212 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08882\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08882","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Quantitative propagation of chaos for non-exchangeable diffusions via first-passage percolation
This paper develops a non-asymptotic approach to mean field approximations
for systems of $n$ diffusive particles interacting pairwise. The interaction
strengths are not identical, making the particle system non-exchangeable. The
marginal law of any subset of particles is compared to a suitably chosen
product measure, and we find sharp relative entropy estimates between the two.
Building upon prior work of the first author in the exchangeable setting, we
use a generalized form of the BBGKY hierarchy to derive a hierarchy of
differential inequalities for the relative entropies. Our analysis of this
complicated hierarchy exploits an unexpected but crucial connection with
first-passage percolation, which lets us bound the marginal entropies in terms
of expectations of functionals of this percolation process.