{"title":"亚临界长程随机聚类和波茨模型中相关函数的尖锐渐近性","authors":"Y. Aoun","doi":"10.1214/21-ECP390","DOIUrl":null,"url":null,"abstract":"For a family of random-cluster models with cluster weights $q\\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\\tfrac{1}{q}\\chi(\\beta)^{2}\\beta J_{0,x}$. The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is one-monotonic.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models\",\"authors\":\"Y. Aoun\",\"doi\":\"10.1214/21-ECP390\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For a family of random-cluster models with cluster weights $q\\\\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\\\\tfrac{1}{q}\\\\chi(\\\\beta)^{2}\\\\beta J_{0,x}$. The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is one-monotonic.\",\"PeriodicalId\":8470,\"journal\":{\"name\":\"arXiv: Probability\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Probability\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/21-ECP390\",\"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-ECP390","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Sharp asymptotics of correlation functions in the subcritical long-range random-cluster and Potts models
For a family of random-cluster models with cluster weights $q\geq 1$, we prove that the probability that $0$ is connected to $x$ is asymptotically equal to $\tfrac{1}{q}\chi(\beta)^{2}\beta J_{0,x}$. The method developed in this article can be applied to any spin model for which there exists a random-cluster representation which is one-monotonic.
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