{"title":"The site frequency spectrum for coalescing Brownian motion","authors":"Yubo Shuai","doi":"10.1016/j.spa.2024.104521","DOIUrl":null,"url":null,"abstract":"<div><div>Motivated by the goal of understanding the genealogy of a sample from an expanding population in the plane, we consider coalescing Brownian motion on the circle. For this model, we establish a weak law of large numbers for the site frequency spectrum. A parallel result holds for a localized version where the genealogy is modeled by coalescing Brownian motion on the line.</div></div>","PeriodicalId":51160,"journal":{"name":"Stochastic Processes and their Applications","volume":"180 ","pages":"Article 104521"},"PeriodicalIF":1.1000,"publicationDate":"2024-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Stochastic Processes and their Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0304414924002291","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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Abstract
Motivated by the goal of understanding the genealogy of a sample from an expanding population in the plane, we consider coalescing Brownian motion on the circle. For this model, we establish a weak law of large numbers for the site frequency spectrum. A parallel result holds for a localized version where the genealogy is modeled by coalescing Brownian motion on the line.
期刊介绍：
Stochastic Processes and their Applications publishes papers on the theory and applications of stochastic processes. It is concerned with concepts and techniques, and is oriented towards a broad spectrum of mathematical, scientific and engineering interests.
Characterization, structural properties, inference and control of stochastic processes are covered. The journal is exacting and scholarly in its standards. Every effort is made to promote innovation, vitality, and communication between disciplines. All papers are refereed.
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