{"title":"On the scaling limits of weakly asymmetric bridges","authors":"C. Labb'e","doi":"10.1214/17-PS285","DOIUrl":null,"url":null,"abstract":"We consider a discrete bridge from ((0,0)) to ((2N,0)) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order (N^{-alpha}) with (alphain(0,infty)). We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter (alpha).\r\n\r\n<script type=\"text/javascript\"\r\nsrc=\"//cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML\">","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2016-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/17-PS285","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
引用次数: 7
Abstract
We consider a discrete bridge from ((0,0)) to ((2N,0)) evolving according to the corner growth dynamics, where the jump rates are subject to an upward asymmetry of order (N^{-alpha}) with (alphain(0,infty)). We provide a classification of the asymptotic behaviours - invariant measure, hydrodynamic limit and fluctuations - of this model according to the value of the parameter (alpha).
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