{"title":"最后通道渗透中的风险风险:统一的方法","authors":"Duncan Dauvergne, M. Nica, B'alint Vir'ag","doi":"10.1214/22-PS4","DOIUrl":null,"url":null,"abstract":": We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two crucial properties for taking limits of last passage percolation models. We use the bijective property to give a non-computational proof that dual RSK maps Bernoulli walks to nonintersecting Bernoulli walks.","PeriodicalId":46216,"journal":{"name":"Probability Surveys","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"RSK in last passage percolation: a unified approach\",\"authors\":\"Duncan Dauvergne, M. Nica, B'alint Vir'ag\",\"doi\":\"10.1214/22-PS4\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two crucial properties for taking limits of last passage percolation models. We use the bijective property to give a non-computational proof that dual RSK maps Bernoulli walks to nonintersecting Bernoulli walks.\",\"PeriodicalId\":46216,\"journal\":{\"name\":\"Probability Surveys\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2021-06-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Probability Surveys\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1214/22-PS4\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Probability Surveys","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1214/22-PS4","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
RSK in last passage percolation: a unified approach
: We present a version of the RSK correspondence based on the Pitman transform and geometric considerations. This version unifies ordinary RSK, dual RSK and continuous RSK. We show that this version is both a bijection and an isometry, two crucial properties for taking limits of last passage percolation models. We use the bijective property to give a non-computational proof that dual RSK maps Bernoulli walks to nonintersecting Bernoulli walks.
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