{"title":"KPZ equation from ASEP plus general speed-change drift","authors":"Kevin Yang","doi":"arxiv-2409.10513","DOIUrl":null,"url":null,"abstract":"We derive the KPZ equation as a continuum limit of height functions in\nasymmetric simple exclusion processes with a hyperbolic-scale drift that\ndepends on the local particle configuration. To our knowledge, it is a first\nsuch result for a general class of particle systems with neither duality nor\nexplicit invariant measures. The new tools to handle the lack of an invariant\nmeasure are estimates for Kolmogorov equations that produce a more robust proof\nof the Kipnis-Varadhan inequality. These tools are not exclusive to KPZ.","PeriodicalId":501245,"journal":{"name":"arXiv - MATH - Probability","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.10513","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We derive the KPZ equation as a continuum limit of height functions in
asymmetric simple exclusion processes with a hyperbolic-scale drift that
depends on the local particle configuration. To our knowledge, it is a first
such result for a general class of particle systems with neither duality nor
explicit invariant measures. The new tools to handle the lack of an invariant
measure are estimates for Kolmogorov equations that produce a more robust proof
of the Kipnis-Varadhan inequality. These tools are not exclusive to KPZ.