{"title":"Exit-time of mean-field particles system","authors":"J. Tugaut","doi":"10.1051/ps/2019028","DOIUrl":null,"url":null,"abstract":"The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain D on ℝd as the diffusion coefficient goes to 0. We establish a Kramers’ type law. In other words, we show that the exit-time is exponentially equivalent to [see formula in PDF], HN being the exit-cost. We also show that this exit-cost converges to some quantity H.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/ps/2019028","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
The current article is devoted to the study of a mean-field system of particles. The question that we are interested in is the behaviour of the exit-time of the first particle (and the one of any particle) from a domain D on ℝd as the diffusion coefficient goes to 0. We establish a Kramers’ type law. In other words, we show that the exit-time is exponentially equivalent to [see formula in PDF], HN being the exit-cost. We also show that this exit-cost converges to some quantity H.