{"title":"湮没分支布朗运动","authors":"Daniel Ahlberg, Omer Angel, Brett Kolesnik","doi":"10.1093/imrn/rnae068","DOIUrl":null,"url":null,"abstract":"We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.","PeriodicalId":14461,"journal":{"name":"International Mathematics Research Notices","volume":"20 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Annihilating Branching Brownian Motion\",\"authors\":\"Daniel Ahlberg, Omer Angel, Brett Kolesnik\",\"doi\":\"10.1093/imrn/rnae068\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.\",\"PeriodicalId\":14461,\"journal\":{\"name\":\"International Mathematics Research Notices\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Mathematics Research Notices\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1093/imrn/rnae068\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Mathematics Research Notices","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1093/imrn/rnae068","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We study an interacting system of competing particles on the real line. Two populations of positive and negative particles evolve according to branching Brownian motion. When opposing particles meet, their charges neutralize and the particles annihilate, as in an inert chemical reaction. We show that, with positive probability, the two populations coexist and that, on this event, the interface is asymptotically linear with a random slope. A variety of generalizations and open problems are discussed.
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International Mathematics Research Notices provides very fast publication of research articles of high current interest in all areas of mathematics. All articles are fully refereed and are judged by their contribution to advancing the state of the science of mathematics.
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