{"title":"Weak convergence of directed polymers to deterministic KPZ at high temperature","authors":"S. Chatterjee","doi":"10.1214/22-aihp1287","DOIUrl":null,"url":null,"abstract":"It is shown that when $d\\ge 3$, the growing random surface generated by the $(d+1)$-dimensional directed polymer model at sufficiently high temperature, after being smoothed by taking microscopic local averages, converges to a solution of the deterministic KPZ equation in a suitable scaling limit.","PeriodicalId":42884,"journal":{"name":"Annales de l Institut Henri Poincare D","volume":null,"pages":null},"PeriodicalIF":1.5000,"publicationDate":"2021-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de l Institut Henri Poincare D","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-aihp1287","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 6
Abstract
It is shown that when $d\ge 3$, the growing random surface generated by the $(d+1)$-dimensional directed polymer model at sufficiently high temperature, after being smoothed by taking microscopic local averages, converges to a solution of the deterministic KPZ equation in a suitable scaling limit.