{"title":"非负次临界势对Gibbs分布的唯一性","authors":"Steffen Betsch, G. Last","doi":"10.1214/22-AIHP1265","DOIUrl":null,"url":null,"abstract":"We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":"1 1","pages":""},"PeriodicalIF":1.5000,"publicationDate":"2021-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential\",\"authors\":\"Steffen Betsch, G. Last\",\"doi\":\"10.1214/22-AIHP1265\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.\",\"PeriodicalId\":42884,\"journal\":{\"name\":\"Annales de l Institut Henri Poincare D\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.5000,\"publicationDate\":\"2021-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de l Institut Henri Poincare D\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/22-AIHP1265\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-AIHP1265","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential
We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.
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