{"title":"离散随机变量的熵中心极限定理","authors":"Lampros Gavalakis, I. Kontoyiannis","doi":"10.1109/ISIT50566.2022.9834855","DOIUrl":null,"url":null,"abstract":"An information-theoretic proof of a strengthened version of the classical discrete central limit theorem is presented. Using only information-theoretic and elementary arguments, convergence to zero of the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian is established.","PeriodicalId":348168,"journal":{"name":"2022 IEEE International Symposium on Information Theory (ISIT)","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Entropic Central Limit Theorem for Discrete Random Variables\",\"authors\":\"Lampros Gavalakis, I. Kontoyiannis\",\"doi\":\"10.1109/ISIT50566.2022.9834855\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An information-theoretic proof of a strengthened version of the classical discrete central limit theorem is presented. Using only information-theoretic and elementary arguments, convergence to zero of the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian is established.\",\"PeriodicalId\":348168,\"journal\":{\"name\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"volume\":\"80 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-06-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2022 IEEE International Symposium on Information Theory (ISIT)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ISIT50566.2022.9834855\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2022 IEEE International Symposium on Information Theory (ISIT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ISIT50566.2022.9834855","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Entropic Central Limit Theorem for Discrete Random Variables
An information-theoretic proof of a strengthened version of the classical discrete central limit theorem is presented. Using only information-theoretic and elementary arguments, convergence to zero of the relative entropy between the standardised sum of n independent and identically distributed lattice random variables and an appropriately discretised Gaussian is established.
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