{"title":"条件高尔顿-沃森树的一般子树","authors":"S. Janson","doi":"10.1214/21-ECP392","DOIUrl":null,"url":null,"abstract":"We show that the number of copies of a given rooted tree in a conditioned Galton-Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":"49 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"On general subtrees of a conditioned Galton–Watson tree\",\"authors\":\"S. Janson\",\"doi\":\"10.1214/21-ECP392\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the number of copies of a given rooted tree in a conditioned Galton-Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":\"49 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/21-ECP392\",\"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: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/21-ECP392","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On general subtrees of a conditioned Galton–Watson tree
We show that the number of copies of a given rooted tree in a conditioned Galton-Watson tree satisfies a law of large numbers under a minimal moment condition on the offspring distribution.