{"title":"Degenerate competing three-particle systems","authors":"Tomoyuki Ichiba, I. Karatzas","doi":"10.3150/21-bej1411","DOIUrl":null,"url":null,"abstract":"We study systems of three interacting particles, in which drifts and\nvariances are assigned by rank. These systems are \"degenerate\": the variances\ncorresponding to one or two ranks can vanish, so the corresponding ranked\nmotions become ballistic rather than diffusive. Depending on which ranks are\nallowed to \"go ballistic\", the systems exhibit markedly different behavior\nwhich we study in some detail. Also studied are stability properties for the\nresulting planar process of gaps between successive ranks.","PeriodicalId":8470,"journal":{"name":"arXiv: Probability","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Probability","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3150/21-bej1411","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
Abstract
We study systems of three interacting particles, in which drifts and
variances are assigned by rank. These systems are "degenerate": the variances
corresponding to one or two ranks can vanish, so the corresponding ranked
motions become ballistic rather than diffusive. Depending on which ranks are
allowed to "go ballistic", the systems exhibit markedly different behavior
which we study in some detail. Also studied are stability properties for the
resulting planar process of gaps between successive ranks.
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