{"title":"Haagerup’s phase transition at polydisc slicing","authors":"Giorgos Chasapis, Salil Singh, Tomasz Tkocz","doi":"10.2140/apde.2024.17.2509","DOIUrl":null,"url":null,"abstract":"<p>We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz–Pełczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the <math display=\"inline\" xmlns=\"http://www.w3.org/1998/Math/MathML\"><mi>p</mi></math>-norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions. </p>","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":"58 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2024.17.2509","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We establish a sharp comparison inequality between the negative moments and the second moment of the magnitude of sums of independent random vectors uniform on three-dimensional Euclidean spheres. This provides a probabilistic extension of the Oleszkiewicz–Pełczyński polydisc slicing result. The Haagerup-type phase transition occurs exactly when the -norm recovers volume, in contrast to the real case. We also obtain partial results in higher dimensions.
期刊介绍:
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