Trigonometric multiplicative chaos and applications to random distributions

作     者：Aihua Fan Yves Meyer 

作者机构：School of Mathematics and StatisticsCentral China Normal UniversityWuhan 430079China LAMFACNRSUMR7352University of PicardieAmiens 80039France CMLAENS-CachanCNRSUniversityof Paris-SaclayParis 91190France 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2023年第66卷第1期

页      面：3-36页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No.11971192) 

主　　题：multiplicative chaos random Fourier series Hausdorff dimension Riesz potential 

摘      要：The random trigonometric series∑∞n=1ρn cos(nt+ωn)on the circle T are studied under the conditions∑|ρn|^(2)=∞andρn→0,where{ωn}are independent and uniformly distributed random variables on *** are almost surely not Fourier-Stieltjes series but determine *** leads us to develop the theory of trigonometric multiplicative chaos,which produces a class of random *** kernel and the image of chaotic operators are fully studied and the dimensions of chaotic measures are exactly *** behavior of the partial sums of the above series is proved to be *** theory holds on the torus Tdof dimension d≥1.