{"title":"Counting Zeros of Random Functions","authors":"L. Nicolaescu","doi":"10.1080/00029890.2023.2206321","DOIUrl":null,"url":null,"abstract":"Abstract What is the expected number of roots of a polynomial whose coefficients are random? More generally, what is the expected number of zeros of a random one-variable function? The Kac-Rice formula is meant to answer such questions. This paper is an introduction to this less familiar formula and some of its one-dimensional applications.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/00029890.2023.2206321","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract What is the expected number of roots of a polynomial whose coefficients are random? More generally, what is the expected number of zeros of a random one-variable function? The Kac-Rice formula is meant to answer such questions. This paper is an introduction to this less familiar formula and some of its one-dimensional applications.
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