{"title":"圆盘多边形的方差界","authors":"F. Fodor, B. Grunfelder, V. V'igh","doi":"10.4171/dm/891","DOIUrl":null,"url":null,"abstract":"We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is $C_+^2$ smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\\'{\\i}gh (2018).","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"20 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Variance bounds for disc-polygons\",\"authors\":\"F. Fodor, B. Grunfelder, V. V'igh\",\"doi\":\"10.4171/dm/891\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is $C_+^2$ smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\\\\'{\\\\i}gh (2018).\",\"PeriodicalId\":50567,\"journal\":{\"name\":\"Documenta Mathematica\",\"volume\":\"20 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-11-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Documenta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/dm/891\",\"RegionNum\":3,\"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":"Documenta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/dm/891","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove asymptotic lower bounds on the variance of the number of vertices and missed area of random disc-polygons in convex discs whose boundary is $C_+^2$ smooth. The established lower bounds are of the same order as the upper bounds proved previously by Fodor and V\'{\i}gh (2018).
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DOCUMENTA MATHEMATICA is open to all mathematical fields und internationally oriented
Documenta Mathematica publishes excellent and carefully refereed articles of general interest, which preferably should rely only on refereed sources and references.
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