{"title":"FKG 对多个事件的强烈不平等性","authors":"Nikita Gladkov","doi":"10.1112/blms.13101","DOIUrl":null,"url":null,"abstract":"<p>We extend the Fortuin–Kasteleyn–Ginibre (FKG) inequality to cover multiple events with equal pairwise intersections. We then apply this inequality to resolve Kahn's question on positive associated measures, as well as prove new inequalities concerning random graphs and probabilities of connection in Bernoulli percolation.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 9","pages":"2794-2801"},"PeriodicalIF":0.8000,"publicationDate":"2024-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13101","citationCount":"0","resultStr":"{\"title\":\"A strong FKG inequality for multiple events\",\"authors\":\"Nikita Gladkov\",\"doi\":\"10.1112/blms.13101\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We extend the Fortuin–Kasteleyn–Ginibre (FKG) inequality to cover multiple events with equal pairwise intersections. We then apply this inequality to resolve Kahn's question on positive associated measures, as well as prove new inequalities concerning random graphs and probabilities of connection in Bernoulli percolation.</p>\",\"PeriodicalId\":55298,\"journal\":{\"name\":\"Bulletin of the London Mathematical Society\",\"volume\":\"56 9\",\"pages\":\"2794-2801\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13101\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the London Mathematical Society\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/blms.13101\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13101","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We extend the Fortuin–Kasteleyn–Ginibre (FKG) inequality to cover multiple events with equal pairwise intersections. We then apply this inequality to resolve Kahn's question on positive associated measures, as well as prove new inequalities concerning random graphs and probabilities of connection in Bernoulli percolation.
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